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In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another
Adjunction_space
Index of articles associated with the same name
Adjoint functors in category theory Adjunction (field theory) Adjunction formula (algebraic geometry) Adjunction space in topology Conjugate transpose of
Adjoint
Concept in algebraic geometry
especially in algebraic geometry and the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside
Adjunction_formula
Topological space construction
the sphere S 2 . {\displaystyle S^{2}.} Adjunction space. More generally, suppose X {\displaystyle X} is a space and A {\displaystyle A} is a subspace of
Quotient_space_(topology)
Relationship between two functors abstracting many common constructions
equivalence gives an adjunction, though the equivalence itself is not necessarily an adjunction. In many situations, an adjunction can be "upgraded" to
Adjoint_functors
Most general completion of a commutative square given two morphisms with same domain
map we can "glue" Y to another space X along Z using an "attaching map" f : Z → X. The result is the adjunction space X ∪ f Y {\displaystyle X\cup _{f}Y}
Pushout_(category_theory)
Operation in algebra and mathematics
mentioned above, any adjunction gives rise to a monad. Conversely, every monad arises from some adjunction, namely the free–forgetful adjunction T ( − ) : C ⇄
Monad_(category_theory)
European organisation dedicated to space exploration
The European Space Agency (ESA; pronounced /ˈiːsə/ EE-sə) is a 23-member international organisation devoted to space exploration. It has its headquarters
European_Space_Agency
Topological space
right adjoint to the reduced suspension. This adjunction accounts for much of the importance of loop spaces in stable homotopy theory. (A related phenomenon
Loop_space
Adjunction between a category of co/presheaf under the co/Yoneda embedding
In mathematics, Isbell conjugacy (a.k.a. Isbell duality or Isbell adjunction) (named after John R. Isbell) is a fundamental construction of enriched category
Isbell_duality
Concept in mathematics
In mathematics, the tensor-hom adjunction is the statement that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ( X , − ) {\displaystyle
Tensor–hom_adjunction
Concept in mathematics
and is an example of Eckmann–Hilton duality. This adjunction is a special case of the adjunction explained in the article on smash products. The reduced
Suspension_(topology)
List of concrete topologies and topological spaces
Tychonoff plank Vague topology Warsaw circle List of natural topologies. Adjunction space Disjoint union (topology) Extension topology Initial topology Final
List_of_topologies
Fictional character in Star Trek franchise
starship Voyager. Her full Borg designation was Seven of Nine, Tertiary Adjunct of Unimatrix Zero One. While her birth name became known to her crewmates
Seven_of_Nine
Relationship between certain categories
verify that for every space X, Ω(X) is spatial and for every locale L, pt(L) is sober. Hence, it follows that the above adjunction of Top and Loc restricts
Stone_duality
Category whose objects are topological spaces and whose morphisms are continuous maps
limits with the final topology and initial topology respectively. Adjunction spaces are an example of pushouts in T o p {\displaystyle \mathbf {Top} }
Category of topological spaces
Category_of_topological_spaces
Category theory
two extremal solutions to the question: "Does every monad arise from an adjunction?" The other extremal solution is the Eilenberg–Moore category. Kleisli
Kleisli_category
Algebraic topology uses abstract algebra to study topological spaces
Wedge sum Smash product Adjunction space Cohomotopy Cohomotopy group Brown's representability theorem Eilenberg–MacLane space Fibre bundle Möbius strip
List of algebraic topology topics
List_of_algebraic_topology_topics
Law governing activities in outer space
Space law or astrolaw is the body of law governing space-related activities, encompassing both international and domestic agreements, rules, and principles
Space_law
Pointed space Wedge sum Smash product Cone (topology) Adjunction space Topological algebra Topological group Topological ring Topological vector space Topological
List of general topology topics
List_of_general_topology_topics
2023 book by Kelly and Zach Weinersmith
A City on Mars: Can We Settle Space, Should We Settle Space, and Have We Really Thought This Through? is a 2023 popular science book by Kelly and Zach
A_City_on_Mars
Greek sculptor (born 1964)
installation artist and former adjunct professor of fine art. She is the co-founder of the non-profit organisation Vital Space. Between 1983 and 1988, Stratou
Danae_Stratou
Tool to track locally defined data attached to the open sets of a topological space
the category of presheaves, and i {\displaystyle i} is the unit of the adjunction. In this way, the category of sheaves turns into a Giraud subcategory
Sheaf_(mathematics)
Mathematical category with weak equivalences, fibrations and cofibrations
equivalence then). A typical example is the standard adjunction between simplicial sets and topological spaces: | − | : s S e t ⇆ T o p : S i n g {\displaystyle
Model_category
Concept in category theory
unit and counit of the adjunction are monoidal natural transformations, and the adjunction is said to be a monoidal adjunction; conversely, the left adjoint
Monoidal_functor
Goddard Space Flight Center (GSFC) is NASA's first, and oldest, space center. It is named after Robert H. Goddard, the father of modern rocketry. Throughout
History of the Goddard Space Flight Center
History_of_the_Goddard_Space_Flight_Center
Exceptional functor
the homology of the base to itself, analogous to a unit/counit of an adjunction; compare also Galois connection. These can be used in understanding and
Shriek_map
Process of assembling the International Space Station
The process of assembling the International Space Station (ISS) has been under way since the 1990s. Zarya, the first ISS module, was launched by a Proton
Assembly of the International Space Station
Assembly_of_the_International_Space_Station
Mathematical concept
equivalence classes is sometimes called the quotient set or the quotient space of S {\displaystyle S} by ∼ , {\displaystyle \sim ,} and is denoted by S
Equivalence_class
Theorem in classical algebraic geometry
. The genus–degree formula can be proved from the adjunction formula; for details, see Adjunction formula § Applications to curves. For a non-singular
Genus–degree_formula
Categorical generalization of a function space in set theory
is an alternative notation for Z Y {\displaystyle Z^{Y}} . The above adjunction results translate to implication ( ⇒: H × H → H {\displaystyle \Rightarrow
Exponential_object
Equivalence between the categories of chain complexes and simplicial abelian groups
special type of adjunction, called the nerve-realization paradigm (also called a nerve-realization context) where the data of this adjunction is determined
Dold–Kan_correspondence
in 1960, is in short the fixed-point category of the Isbell conjugacy adjunction. It should not be confused with the Isbell envelope, which was also introduced
Completions in category theory
Completions_in_category_theory
American actor (born 1953)
After graduating with a Master of Fine Arts degree in theater, he was an adjunct professor at Montana State University before deciding to pursue acting
Bill_Pullman
Riemannian manifold with SU(n) holonomy
complete intersections in a weighted projective space. The main tool for finding such spaces is the adjunction formula. All hyper-Kähler manifolds are Calabi–Yau
Calabi–Yau_manifold
Branch of mathematics
is an analog of a tensor product in abstract algebra (see tensor-hom adjunction). Explicitly, X ∧ Y {\displaystyle X\wedge Y} is the quotient of X × Y
Homotopy_theory
Eilenberg–MacLane spaces { K ( A , 0 ) , K ( A , 1 ) , K ( A , 2 ) , … } {\displaystyle \{K(A,0),K(A,1),K(A,2),\ldots \}} with the adjunction map coming from
Eilenberg–MacLane_spectrum
Religious context during spaceflights
observed their religions while in space; sometimes publicly, sometimes privately. Religious adherence in outer space may pose unique challenges and opportunities
Religion_in_space
Endofunctor on the category of simplicial sets
structure. This makes the adjunction Sd ⊣ Ex {\displaystyle \operatorname {Sd} \dashv \operatorname {Ex} } even into a Quillen adjunction Sd : s S e t K Q ⇄
Extension_(simplicial_set)
Mathematical concept
this adjunction is simply the universal cone from lim F to F. If the index category J is connected (and nonempty) then the unit of the adjunction is an
Limit_(category_theory)
Transforming a function in such a way that it only takes a single argument
the relationship between currying and uncurrying is known as tensor-hom adjunction. Here, an interesting twist arises: the Hom functor and the tensor product
Currying
Homological construction in category theory
topological spaces and the category of simplicial sets both admit Quillen model structures whose nerve and realization adjunction gives a Quillen adjunction that
Derived_functor
Concept in algebraic geometry
D {\displaystyle D} is a smooth divisor on X {\displaystyle X} . The adjunction formula relates the canonical bundles of X {\displaystyle X} and D {\displaystyle
Canonical_bundle
Concept in mathematical theory of categories
the reflector. The map r B {\displaystyle r_{B}} is the unit of this adjunction. The reflector assigns to B {\displaystyle B} the A-object A B {\displaystyle
Reflective_subcategory
Combination of pointed topological spaces
formula: if A , X {\displaystyle A,X} are compact Hausdorff then we have an adjunction M a p s ∗ ( X ∧ A , Y ) ≅ M a p s ∗ ( X , M a p s ∗ ( A , Y ) ) {\displaystyle
Smash_product
Country in Eastern Europe and North Asia
Roscosmos is Russia's national space agency. The country's achievements in the field of space technology and space exploration can be traced back to
Russia
American astronaut and engineer (born 1955)
responsibilities involved reviewing materials used in Space Shuttle payloads. In 1988 he joined NASA's Lyndon B. Johnson Space Center as a materials engineer. His work
Donald_A._Thomas
Sheaf theory
category of locally constant sheaves on X. If X is locally connected, the adjunction between the category of presheaves and bundles restricts to an equivalence
Locally_constant_sheaf
German-American rocket engineer and scientist (1908–1983)
services, range activities, space education and spaceport research and development. The award was conceived as an adjunct to the Goddard Award given each
Kurt_Debus
Central object of study in category theory
Ab {\displaystyle {\textbf {Ab}}} !) This is formally the tensor-hom adjunction, and is an archetypal example of a pair of adjoint functors. Natural transformations
Natural_transformation
Generalization of a category
{\textbf {Kan}}} (recall the mapping spaces are Kan complexes). In his book Higher Topos Theory, Lurie defines an adjunction to be a map q : M → Δ 1 {\displaystyle
Quasi-category
American physicist (1941–2025)
was an American physicist who was professor emeritus of history and an adjunct professor of physics at California State University, Fullerton. He is best
James_Woodward_(physicist)
Conversion of a matrix or a tensor to a vector
is a self-adjunction in the monoidal closed structure of any category of matrices. Vectorization is an algebra homomorphism from the space of n × n matrices
Vectorization_(mathematics)
American astronaut and politician (1921–2016)
aviator, astronaut, businessman, and politician. He was the third American in space and the first to orbit the Earth, circling it three times in 1962. Following
John_Glenn
American actor (born 1949)
franchise, appearing as the character in all seven seasons of Star Trek: Deep Space Nine (1993–1999). He also had a recurring role as Principal Snyder in the
Armin_Shimerman
Theory of rapid universe expansion
cosmological inflation, or just inflation, is a theory of exponential expansion of space in the very early universe. This enormous expansion supercooled the universe
Cosmic_inflation
]} . By adjunction we can add a unit to the convolution in C [ [ ζ ] ] {\displaystyle \mathbb {C} [[\zeta ]]} and introduce the vector space C × C [ [
Resurgent_function
given small category C , {\displaystyle C,} Isbell duality refers to the adjunction O : S e t C o p ⇄ ( S e t C ) o p : S p e c {\displaystyle {\mathcal
Codensity_monad
American astronaut (born 1956)
as adjunct professor in the Department of Space Physics and Astronomy at Rice University. That same year he came to work at NASA’s Johnson Space Center
James_H._Newman
{\displaystyle p_{g}-1\leq h^{0}(K|_{D}).} Assume that D is smooth. By the adjunction formula D has a canonical linebundle O D ( 2 K ) {\displaystyle {\mathcal
Noether_inequality
Mathematical construction used in homotopy theory
topological space Y. Intuitively, this adjunction can be understood as follows: a continuous map from the geometric realization of X to a space Y is uniquely
Simplicial_set
Theorem on extension of bounded linear functionals
some suitable space of test functions g , {\displaystyle g,} then we can view f {\displaystyle f} as a linear functional by adjunction: ( f , g ) = (
Hahn–Banach_theorem
1995 American science fiction television series
overlap with Deep Space Nine and to maintain thematic continuity with elements that had been introduced in The Next Generation and Deep Space Nine. The complex
Star_Trek:_Voyager
American astronaut, first woman to circle the Moon (born 1979)
American engineer and NASA astronaut. On her mission to the International Space Station in 2019–20 she was part of the first all‑female spacewalk and set
Christina_Koch
Branch of logic using category theory to study mathematical structures
to the category of theories in that logic by an adjunction, where the two functors in the adjunction give the internal language of a structured category
Categorical_logic
American astronaut and biochemistry researcher (born 1960)
is an American biochemistry researcher, and astronaut working for Axiom Space. She retired from NASA in 2018, after serving as the 13th chief of the Astronaut
Peggy_Whitson
Duality between the process of restricting and inducting in representation theory
they are actually both left- and right-adjoint to one another. This adjunction gives rise to a universal property for the induced representation (for
Frobenius_reciprocity
American space weather physicist
research scientist at The Aerospace Corporation and as an adjunct professor of heliophysics and space weather at Millerville University. Skov holds an amateur
Tamitha_Skov
Private art college in the US
leased space in the building starting in 1997 and purchased the structure in 1999. It currently houses administrative offices, classroom space and the
Columbia_College_Chicago
Concept in algebraic geometry
symplectic form). Let D be a smooth codimension-1 subvariety in Pn. The adjunction formula implies that KD = (KX + D)|D = (−(n+1)H + deg(D)H)|D, where H
Fano_variety
American physician and astronaut (born 1935)
Lee Morin. Musgrave is the only astronaut to have flown aboard all five Space Shuttle orbiters. Musgrave was born August 19, 1935, the son of Percy Musgrave
Story_Musgrave
American astronaut and professor (born 1952)
Physics at the University of Houston, affiliated with the Space Vacuum Epitaxy Center, and is adjunct professor of physics. Sega is a co-principal investigator
Ronald_M._Sega
1791 amendment protecting the right to keep and bear arms
Association, Inc. v. Bruen (2022) assured the right to carry weapons in public spaces with certain exceptions. The Second Amendment was based partially on the
Second Amendment to the United States Constitution
Second_Amendment_to_the_United_States_Constitution
Public university in Los Angeles, California, U.S.
the state college upper division classes were being taught in borrowed spaces on the City College campus by mostly part-time faculty. He hired administrators
California State University, Los Angeles
California_State_University,_Los_Angeles
American astronaut and engineer (born 1962)
former NASA astronaut. He is the senior advisor of space programs at the Intrepid Sea, Air & Space Museum. Massimino was born August 19, 1962, in Oceanside
Mike_Massimino
Chinese multinational technology company
releases of variants, marking Huawei entrance into the workstation, desktop PC space with All-in-one and Thin client PCs. The Huawei Watch is an Android Wear-based
Huawei
Theory in algebraic topology
informal relationships is given by Fuks duality. Model category Tensor-hom adjunction Eckmann-Hilton duality at the nLab Hatcher, Allen (2002), Algebraic Topology
Eckmann–Hilton_duality
National airline of Russia
related to air ambulance; aerial application; heavy lifting for the Soviet space program; offshore oil platform support; exploration and aeromagnetic survey
Aeroflot
-P. Demailly, $L^2$ vanishing theorems for positive line bundles and adjunction theory, Lecture Notes of a CIME course on "Transcendental Methods of Algebraic
Positive_current
Algebraic structure with "nice" duality properties
abstraction to ordinary category theory: An adjunction F ⊣ G {\displaystyle F\dashv G} is called a Frobenius adjunction iff also G ⊣ F {\displaystyle G\dashv
Frobenius_algebra
Prepositions in the English language
, in the water). Semantically, they most typically denote relations in space and time. Morphologically, they are usually simple and do not inflect. They
English_prepositions
American architect and academic (1910–1989)
1910 – July 31, 1989) was an American educator, lecturer, author, and an adjunct professor of architecture and art history at Columbia University. He was
Edgar_Kaufmann_Jr.
American astrophysicist and cosmologist (born 1946)
Mather is a senior astrophysicist at the NASA Goddard Space Flight Center (GSFC) in Maryland and adjunct professor of physics at the University of Maryland
John_C._Mather
Mathematical logician and philosopher
more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its
Kurt_Gödel
International agreement on the nuclear program of Iran
infrastructure". Similar arguments have been advanced by Mark Jansson, adjunct fellow at the Federation of American Scientists (who wrote in October 2013
Iran_nuclear_deal
American politician (born 1954)
and the Natural Resources Defense Council (NRDC). In 1986, he became an adjunct professor of environmental law at Pace University School of Law, and in
Robert_F._Kennedy_Jr.
1845–48 British failed Arctic exploration
written largely on the margins of the form owing to a lack of remaining space on the document. It was presumably written on 25 April 1848.[citation needed]
Franklin's_lost_expedition
Construction in algebraic topology
f^{-1}f_{*}{\mathcal {F}}\rightarrow {\mathcal {F}}} . These morphisms yield a natural adjunction correspondence: H o m S h ( X ) ( f − 1 G , F ) = H o m S h ( Y ) ( G
Inverse_image_functor
Persistent representation of language
complement and extend the capacities of spoken language, transmitting it across space (e.g. written correspondence) and storing it for future reading (e.g. libraries)
Writing
American futurist and journalist
author and founder and CEO of the Future Today Strategy Group. She is an adjunct assistant professor at New York University's Stern School of Business,
Amy_Webb
Shooting of a firearm into the air in celebration
International Criminal Tribunal for the former Yugoslavia. "Nurse and Adjunct Professor, 61, Killed by Celebratory Gunfire in Texas on New Year's Day"
Celebratory_gunfire
American electrical engineer and astronaut (1930–2019)
spent 60 days aboard the Skylab space station in 1973 during the Skylab 3 mission, and 10 days aboard Spacelab-1 on a Space Shuttle mission in 1983. After
Owen_Garriott
American advocate (1920–2020)
decided to become involved in the Space Race and launch Project Mercury. Seven young men were chosen for this space mission. These all-American astronauts
Annie_Glenn
Synthetic opioid pain medication
divided into one 100-mg dose every 6 hours (i.e., four 100-mg doses evenly spaced out per day). Some accumulation of tramadol occurs with chronic administration;
Tramadol
Australian architect
solicitors, Gaden, Bowen and Stewart, who occupied the first floor, and office space for lease on the second floor, eight shops on the ground floor and a large
Neville_Gruzman
Plane tiling corresponding to a polyhedron
projective polytopes (tilings that cover projective space twice), whose cover (corresponding to the adjunction of the connection) is a compound of two polytopes
Projective_polyhedron
Pay and benefits for upper management
planning, home security systems, club memberships, sports tickets, office space, secretarial help, and cell phone service. Unremarked upon when they are
Executive compensation in the United States
Executive_compensation_in_the_United_States
Seventh letter in the Greek alphabet
function, and Weierstrass eta function. In category theory, the unit of an adjunction or monad is usually denoted η. Biology, a DNA polymerase found in higher
Eta
American music journalist and author
Liz Pelly is an American writer, journalist, and adjunct professor at New York University. Her book Mood Machine: The Rise of Spotify and the Costs of
Liz_Pelly
Chemical compound
total creatine stores An approximation of 0.3 g/kg/day divided into 4 equal spaced intervals has been suggested since creatine needs may vary based on body
Creatine
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