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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
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
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
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
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
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)
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
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
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
Area of national and international 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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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. Stratou is also known as the
Danae_Stratou
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
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
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
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
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
American politician (born 1969)
2009 to seek a seat on the New York City Council. Lander teaches as an adjunct professor at Brooklyn Law School. Lander represented the 39th district
Brad_Lander
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
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)
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
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)
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
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
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
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
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
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
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
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
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
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
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 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)
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
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
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
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
Historical Hindu practice of widow immolation
reason for her existence according to many classical Hindu texts. Feminist Spaces: Gender and Geography in a Global Context, Routledge, Ann M. Oberhauser
Sati_(practice)
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
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
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
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
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
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
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
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
American lawyer and politician (born 1958)
regular pro bono work. In 1988, he started teaching legal ethics as an adjunct professor at the University of Richmond School of Law. Kaine taught at
Tim_Kaine
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
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
Medical facility
and social response to drug-related problems. They are fixed or mobile spaces where people who use drugs are provided with sterile drug use equipment
Supervised_injection_site
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
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)
]} . 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
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
Category whose objects are measurable spaces and whose morphisms are Markov kernels
of measurable spaces. The left adjoint L : M e a s → S t o c h {\displaystyle L:\mathrm {Meas} \to \mathrm {Stoch} } of the adjunction above is the identity
Category_of_Markov_kernels
Indian economist and Nobel laureate (born 1933)
1959. The work had been completed earlier, except for advice from his adjunct supervisor in India, A. K. Dasgupta, given to Sen while teaching and revising
Amartya_Sen
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
2023 adventure video game
known as "the Swan". The player is equipped with a Personal Maintenance Adjunct, a mechanical gauntlet that allows them to interface with sockets for opening
Firmament_(video_game)
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
Theory and technique for handling geometrical structures
connection are called "adjunctions", and the erosion is said to be the adjoint erosion of the dilation, and vice versa. For every adjunction ( ε , δ ) {\displaystyle
Mathematical_morphology
American sports executive
principal of investment firm Neivel Capital and 82nd Street Partners and an adjunct professor of law at the University of Michigan Law School. His net worth
Jason_Levien
Name list
Steinberger, American trial lawyer and founder of law firm, judge pro tem, adjunct law professor, TV legal analyst Jeffrey Dahmer (1960–1994), American cannibalistic
Jeffrey_(given_name)
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
American astrophysicist (1928–2023)
Laboratory, University of Arizona, until 2007. He was retired and an adjunct professor of Space Physics at Texas A & M University. At the Possible Relationships
Alexander_J._Dessler
Set of finitely supported functions from a group to a ring
When R = Z, this gives an adjunction between the category of groups and the category of rings, and the unit of the adjunction takes a group G to a group
Group_ring
Physicist and intelligence officer
Defense's All-domain Anomaly Resolution Office (AARO). Kirkpatrick is also an adjunct assistant professor of physics at the University of Georgia. Kirkpatrick
Sean_M._Kirkpatrick
Mapping arbitrary data to fixed-size values
per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing
Hash_function
Secular meditation practice
Guide to Tranquil Wisdom Insight Meditation (PDF). Annapolis, MO: CreateSpace Independent Publishing Platform. p. 4. ISBN 978-1-5085-6971-8. "The Community
Mindfulness
Marvel Comics superhero team of mutants
X-Men books. Space travel has been a common staple in the X-Men books beginning with the Phoenix and Dark Phoenix sagas. Since then space has been involved
X-Men
U.S. academic ranks of assistant professor, associate professor, or professor
Non-tenure-track positions may be full or part time, although the qualifier "adjunct" always denotes part-time (whether combined with the word "professor" or
Professors in the United States
Professors_in_the_United_States
Calculus of functions generalization
normed spaces. Differential geometry of surfaces Integration along fibers Lusin's theorem Density on a manifold This is just the tensor-hom adjunction. Spivak
Calculus_on_Euclidean_space
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
American politician and attorney (born 1951)
Chaffe McCall from 1985 to 1987 and 1992 to 1996. He also served as an adjunct professor at Louisiana State University's Paul M. Hebert Law Center in
John Kennedy (Louisiana politician)
John_Kennedy_(Louisiana_politician)
Generalization of vector bundles
underlying ring, and the adjunction comes from taking global sections. Let f : X → Y {\displaystyle f:X\to Y} be a morphism of ringed spaces (for example, a morphism
Coherent_sheaf
ADJUNCTION SPACE
ADJUNCTION SPACE
Girl/Female
Biblical
Spaces, places.
Boy/Male
Tamil
Limitless space Avatar incarnation
Girl/Female
Maori
Open spaces.
Surname or Lastname
English
English : topographic name for someone who lived by a watercourse or road junction, Old English gelǣt, or a habitational name from Leat in Devon, or The Leete in Essex, named with this element.
Surname or Lastname
English
English : occupational name for a wattler, Middle English watelere, i.e. someone who made the panels of interwoven twigs that were used to fill the spaces between the structural timbers of a timber frame building. See also Dauber.
Boy/Male
Arabic, Muslim, Pashtun
Battle Field; Open Space
Girl/Female
Gujarati, Hindu, Indian
Star in Space
Boy/Male
Hindu
Limitless space Avatar incarnation
Girl/Female
Indian, Telugu
Space
Surname or Lastname
English or Scottish
English or Scottish : unexplained.
Girl/Female
Tamil
Antariksha | அஂதரிகà¯à®·
Space, Sky
Antariksha | அஂதரிகà¯à®·
Boy/Male
Hindu
Space
Boy/Male
Indian
Open space, Battle field
Boy/Male
Biblical
Breadth, space, extent.
Boy/Male
Hindu
Space
Surname or Lastname
English
English : habitational name from either of two places in Cheshire. It is possible that the name originally denoted a building where village assemblies were held, named in Old English as ‘meeting-house’, from (ge)mÅt ‘meeting’ + ærn ‘house’, ‘hall’. Other possibilities are that the name derives from Old English (ge)mÅt-rÅ«m ‘meeting space’, or (ge)mÅt-treum ‘assembly trees’.
Girl/Female
Indian, Telugu
Goddess of Space
Boy/Male
Muslim
Open space, Battle field
Girl/Female
Indian, Japanese, Tamil
Space; Star
Boy/Male
Hindu
Space
ADJUNCTION SPACE
ADJUNCTION SPACE
Boy/Male
Indian
Who Won Every Time
Girl/Female
Australian, Latin
Young; Jove's Child; Female Version of Julius
Boy/Male
English Irish Scottish American Celtic
from the craggy hills.
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Dancer; Suggestive Look
Girl/Female
Muslim/Islamic
A woman worthy of the
Boy/Male
Shakespearean
Cymbeline' Posthumus Leonatus, a gentleman and husband to Imogen.
Boy/Male
Tamil
Being near name of the river
Boy/Male
Indian, Telugu
Son of Siva
Girl/Female
American, Anglo, British, Christian, English, Indian, Jamaican
Noble Strength
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Rajasthani, Tamil, Telugu
Engrossed
ADJUNCTION SPACE
ADJUNCTION SPACE
ADJUNCTION SPACE
ADJUNCTION SPACE
ADJUNCTION SPACE
n.
The act of adjuring; a solemn charging on oath, or under the penalty of a curse; an earnest appeal.
n.
A magisterial injunction.
n.
Junction; adaptation
n.
The act of joining, or the state of being joined; union; combination; coalition; as, the junction of two armies or detachments; the junction of paths.
n.
The act of disjoining, or the state of being disjoined.
n.
A uniting; union.
n.
That which is enjoined; an order; a mandate; a decree; a command; a precept; a direction.
a.
Joining; having the quality of joining; forming an adjunct.
n.
A command; injunction.
n.
The place or point of union, meeting, or junction; specifically, the place where two or more lines of railway meet or cross.
n.
The form of oath or appeal.
n.
The act of enjoining; the act of directing, commanding, or prohibiting.
n.
The act or mode of adding; also, the thing added.
adv.
In an adjunctive manner.
a.
Containing an adjuration.
n.
A writ or process, granted by a court of equity, and, insome cases, under statutes, by a court of law,whereby a party is required to do or to refrain from doing certain acts, according to the exigency of the writ.
n.
The action by which the parts of the body are drawn towards its axis]; -- opposed to abduction.
n.
Command; precept; injunction.
n.
The act of joining; the thing joined or added.
n.
One who, or that which, is joined.