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Category theory
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Mathematics
Fields of mathematics
Fields of abstract algebra
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1970-01-01
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Table of contents
Additive categories
Category theory
Abelian category
Additive categories
Additive category
Additive categories
Biproduct
Additive categories
Double complex
Additive categories
Exact category
Additive categories
Exact functor
Additive categories
Exact sequence
Additive categories
Homotopy category of chain complexes
Additive categories
Pre-abelian category
Additive categories
Preadditive category
Additive categories
Quasi-abelian category
Additive categories
Semi-abelian category
Additive categories
Categories in category theory
Category theory
Axiomatic foundations of topological spaces
Categories in category theory
Category of abelian groups
Categories in category theory
Category of groups
Categories in category theory
Category of manifolds
Categories in category theory
Category of medial magmas
Categories in category theory
Category of metric spaces
Categories in category theory
Category of preordered sets
Categories in category theory
Category of rings
Categories in category theory
Category of sets
Categories in category theory
Category of small categories
Categories in category theory
Category of topological spaces
Categories in category theory
Category of topological vector spaces
Categories in category theory
Comma category
Categories in category theory
Connected category
Categories in category theory
Derived category
Categories in category theory
Differential graded category
Categories in category theory
Discrete category
Categories in category theory
FinSet
Categories in category theory
Fukaya category
Categories in category theory
Functor category
Categories in category theory
Kleisli category
Categories in category theory
Monoid (category theory)
Categories in category theory
Regular category
Categories in category theory
Small set (category theory)
Categories in category theory
Category theorists
Category theory
André Joyal
Category theorists
Andrée Ehresmann
Category theorists
Charles Ehresmann
Category theorists
Charles Rezk
Category theorists
David Spivak
Category theorists
Emily Riehl
Category theorists
Eugenia Cheng
Category theorists
Jacob Lurie
Category theorists
Jacques Feldbau
Category theorists
Jacques Riguet
Category theorists
Jean Bénabou
Category theorists
John C. Baez
Category theorists
John C. Oxtoby
Category theorists
John R. Isbell
Category theorists
Kenneth Brown (mathematician)
Category theorists
Martin Hyland
Category theorists
Max Kelly
Category theorists
Michael Barr (mathematician)
Category theorists
Michael Shulman (mathematician)
Category theorists
Myles Tierney
Category theorists
Peter J. Freyd
Category theorists
Peter Johnstone (mathematician)
Category theorists
Richard J. Wood
Category theorists
Ross Street
Category theorists
Samuel Eilenberg
Category theorists
Urs Schreiber
Category theorists
Valeria de Paiva
Category theorists
Věra Trnková
Category theorists
William Lawvere
Category theorists
Closed categories
Category theory
*-autonomous category
Closed categories
Cartesian closed category
Closed categories
Closed category
Closed categories
Closed monoidal category
Closed categories
Compact closed category
Closed categories
Dagger categories
Category theory
Category of finite-dimensional Hilbert spaces
Dagger categories
Dagger category
Dagger categories
Dagger compact category
Dagger categories
Dagger symmetric monoidal category
Dagger categories
Ribbon category
Dagger categories
Duality theories
Category theory
Adjoint functors
Duality theories
Closure operators
Duality theories
Self-duality
Duality theories
Alvis–Curtis duality
Duality theories
Artin–Verdier duality
Duality theories
Born reciprocity
Duality theories
Convex conjugate
Duality theories
Dual abelian variety
Duality theories
Dual polyhedron
Duality theories
Dual system
Duality theories
Dual wavelet
Duality theories
Duality (electrical circuits)
Duality theories
Duality (electricity and magnetism)
Duality theories
Duality (mathematics)
Duality theories
Duality (mechanical engineering)
Duality theories
Duality (order theory)
Duality theories
Duality (projective geometry)
Duality theories
Esakia duality
Duality theories
Fei–Ranis model of economic growth
Duality theories
Grothendieck local duality
Duality theories
Group scheme
Duality theories
Hodge star operator
Duality theories
Koszul duality
Duality theories
Lefschetz duality
Duality theories
List of dualities
Duality theories
Local Tate duality
Duality theories
Montonen–Olive duality
Duality theories
Noncommutative harmonic analysis
Duality theories
Pontryagin duality
Duality theories
Reflexive space
Duality theories
Riesz representation theorem
Duality theories
Riesz–Markov–Kakutani representation theorem
Duality theories
Seiberg duality
Duality theories
Semi-reflexive space
Duality theories
Six operations
Duality theories
Stone duality
Duality theories
Supporting functional
Duality theories
Tannaka–Krein duality
Duality theories
Tannakian formalism
Duality theories
Tate duality
Duality theories
Verdier duality
Duality theories
Free algebraic structures
Category theory
Free Lie algebra
Free algebraic structures
Free abelian group
Free algebraic structures
Free algebra
Free algebraic structures
Free category
Free algebraic structures
Free group
Free algebraic structures
Free independence
Free algebraic structures
Term algebra
Free algebraic structures
Functors
Category theory
Representable functors
Functors
2-functor
Functors
Amnestic functor
Functors
Derived functor
Functors
Diagram (category theory)
Functors
Dinatural transformation
Functors
Dominant functor
Functors
Effaceable functor
Functors
End (category theory)
Functors
Essentially surjective functor
Functors
Final functor
Functors
Forgetful functor
Functors
Full and faithful functors
Functors
Functor
Functors
Hom functor
Functors
Ind-completion
Functors
Natural transformation
Functors
Polynomial functor
Functors
Presheaf (category theory)
Functors
Profunctor
Functors
Pseudo-functor
Functors
Schur functor
Functors
Smooth functor
Functors
Span (category theory)
Functors
Subfunctor
Functors
Translation functor
Functors
Zuckerman functor
Functors
Higher category theory
Category theory
Bicategory
Higher category theory
Conglomerate (mathematics)
Higher category theory
Extranatural transformation
Higher category theory
Higher Topos Theory
Higher category theory
N-category number
Higher category theory
N-monoid
Higher category theory
Stable ∞-category
Higher category theory
Strict 2-category
Higher category theory
String diagram
Higher category theory
Tetracategory
Higher category theory
Tricategory
Higher category theory
Weak n-category
Higher category theory
∞-topos
Higher category theory
Limits (category theory)
Category theory
Coequalizer
Limits (category theory)
Complete category
Limits (category theory)
Coproduct
Limits (category theory)
Equaliser (mathematics)
Limits (category theory)
Initial and terminal objects
Limits (category theory)
Limit (category theory)
Limits (category theory)
Product (category theory)
Limits (category theory)
Pullback (category theory)
Limits (category theory)
Pushout (category theory)
Limits (category theory)
Objects (category theory)
Category theory
Exponential object
Objects (category theory)
Global element
Objects (category theory)
Group object
Objects (category theory)
List object
Objects (category theory)
Projective object
Objects (category theory)
Strict initial object
Objects (category theory)
Subobject
Objects (category theory)
Subobject classifier
Objects (category theory)
Sheaf theory
Category theory
Geometry of divisors
Sheaf theory
Algebraic analysis
Sheaf theory
Base change theorems
Sheaf theory
Constant sheaf
Sheaf theory
Constructible sheaf
Sheaf theory
Cousin problems
Sheaf theory
D-module
Sheaf theory
De Rham–Weil theorem
Sheaf theory
Direct image functor
Sheaf theory
Direct image with compact support
Sheaf theory
Exceptional inverse image functor
Sheaf theory
Exponential sheaf sequence
Sheaf theory
Flat topology
Sheaf theory
Gabriel–Rosenberg reconstruction theorem
Sheaf theory
Gerbe
Sheaf theory
Germ (mathematics)
Sheaf theory
Grothendieck topology
Sheaf theory
Hyperfunction
Sheaf theory
Ideal sheaf
Sheaf theory
Image functors for sheaves
Sheaf theory
Injective sheaf
Sheaf theory
Inverse image functor
Sheaf theory
Invertible sheaf
Sheaf theory
Leray's theorem
Sheaf theory
Leray cover
Sheaf theory
Leray spectral sequence
Sheaf theory
Locally constant function
Sheaf theory
Reflexive sheaf
Sheaf theory
Restriction (mathematics)
Sheaf theory
Ringed space
Sheaf theory
Ringed topos
Sheaf theory
Sheaf of algebras
Sheaf theory
Sheaf of modules
Sheaf theory
Sheaf on an algebraic stack
Sheaf theory
Stalk (sheaf)
Sheaf theory
Topos
Sheaf theory
Torsion sheaf
Sheaf theory
Étale topos
Sheaf theory
AB5 category
Category theory
Abstract nonsense
Category theory
Accessible category
Category theory
Adhesive category
Category theory
Allegory (mathematics)
Category theory
Anamorphism
Category theory
Applied category theory
Category theory
Beck's monadicity theorem
Category theory
Brown's representability theorem
Category theory
Bundle (mathematics)
Category theory
Burnside category
Category theory
Cartesian monoidal category
Category theory
Categorical quantum mechanics
Category theory
Categorical trace
Category theory
Categories for the Working Mathematician
Category theory
Category algebra
Category theory
Category of representations
Category theory
Center (category theory)
Category theory
Chu space
Category theory
Codensity monad
Category theory
Coherence condition
Category theory
Commutative diagram
Category theory
Compact object (mathematics)
Category theory
Concrete category
Category theory
Cone (category theory)
Category theory
Conservative functor
Category theory
Corestriction
Category theory
Cosmos (category theory)
Category theory
Day convolution
Category theory
Descent (mathematics)
Category theory
Diagonal functor
Category theory
Dialectica space
Category theory
DisCoCat
Category theory
Distributive category
Category theory
Dual (category theory)
Category theory
Duality theory for distributive lattices
Category theory
Element (category theory)
Category theory
Enriched category
Category theory
Envelope (category theory)
Category theory
Equivalence of categories
Category theory
Essential monomorphism
Category theory
Exact completion
Category theory
Extensive category
Category theory
F-algebra
Category theory
F-coalgebra
Category theory
Factorization system
Category theory
Fiber functor
Category theory
Fibred category
Category theory
Filtered category
Category theory
Finitely generated object
Category theory
Freyd cover
Category theory
Fusion category
Category theory
Gamma-object
Category theory
Generator (category theory)
Category theory
Giraud subcategory
Category theory
Globular set
Category theory
Glossary of category theory
Category theory
Graded category
Category theory
Grothendieck's Galois theory
Category theory
Grothendieck's relative point of view
Category theory
Grothendieck category
Category theory
Grothendieck construction
Category theory
Grothendieck universe
Category theory
Groupoid object
Category theory
Hylomorphism (computer science)
Category theory
Image (category theory)
Category theory
Indexed category
Category theory
Indiscrete category
Category theory
Initial algebra
Category theory
Injective cogenerator
Category theory
Injective object
Category theory
Inserter category
Category theory
Internal category
Category theory
Isbell conjugacy
Category theory
Isomorphism-closed subcategory
Category theory
Kan extension
Category theory
Karoubi envelope
Category theory
Kernel (category theory)
Category theory
Krohn–Rhodes theory
Category theory
Krull–Schmidt category
Category theory
Lax functor
Category theory
Lax natural transformation
Category theory
Lift (mathematics)
Category theory
Lifting property
Category theory
Limit and colimit of presheaves
Category theory
List of types of functions
Category theory
Localization of a category
Category theory
Localizing subcategory
Category theory
Mac Lane coherence theorem
Category theory
Monad (category theory)
Category theory
Multicategory
Category theory
Nerve (category theory)
Category theory
Nodal decomposition
Category theory
Opetope
Category theory
Opposite category
Category theory
Outline of category theory
Category theory
Overcategory
Category theory
Permutation category
Category theory
Pointless topology
Category theory
Polyad
Category theory
Polygraph (mathematics)
Category theory
Posetal category
Category theory
Product category
Category theory
Pseudo-abelian category
Category theory
Pulation square
Category theory
Q-category
Category theory
Quantaloid
Category theory
Quiver (mathematics)
Category theory
Quotient category
Category theory
Quotient of an abelian category
Category theory
Refinement (category theory)
Category theory
Section (category theory)
Category theory
Segal category
Category theory
Segal space
Category theory
Semiautomaton
Category theory
Sieve (category theory)
Category theory
Simplicial localization
Category theory
Simplicially enriched category
Category theory
Skeleton (category theory)
Category theory
Sketch (mathematics)
Category theory
Spherical category
Category theory
Stable model category
Category theory
Stack (mathematics)
Category theory
Subcategory
Category theory
Subterminal object
Category theory
Symplectic category
Category theory
T-structure
Category theory
Timeline of category theory and related mathematics
Category theory
Topological category
Category theory
Tower of objects
Category theory
Universal property
Category theory
Waldhausen category
Category theory
Well-pointed category
Category theory
Additive categories
0
0
0
Category theory
Abelian category
0
0
0
Additive categories
Additive category
0
0
0
Additive categories
Biproduct
0
0
0
Additive categories
Double complex
0
0
0
Additive categories
Exact category
0
0
0
Additive categories
Exact functor
0
0
0
Additive categories
Exact sequence
0
0
0
Additive categories
Homotopy category of chain complexes
0
0
0
Additive categories
Pre-abelian category
0
0
0
Additive categories
Preadditive category
0
0
0
Additive categories
Quasi-abelian category
0
0
0
Additive categories
Semi-abelian category
0
0
0
Additive categories
Categories in category theory
0
0
0
Category theory
Axiomatic foundations of topological spaces
0
0
0
Categories in category theory
Category of abelian groups
0
0
0
Categories in category theory
Category of groups
0
0
0
Categories in category theory
Category of manifolds
0
0
0
Categories in category theory
Category of medial magmas
0
0
0
Categories in category theory
Category of metric spaces
0
0
0
Categories in category theory
Category of preordered sets
0
0
0
Categories in category theory
Category of rings
0
0
0
Categories in category theory
Category of sets
0
0
0
Categories in category theory
Category of small categories
0
0
0
Categories in category theory
Category of topological spaces
0
0
0
Categories in category theory
Category of topological vector spaces
0
0
0
Categories in category theory
Comma category
0
0
0
Categories in category theory
Connected category
0
0
0
Categories in category theory
Derived category
0
0
0
Categories in category theory
Differential graded category
0
0
0
Categories in category theory
Discrete category
0
0
0
Categories in category theory
FinSet
0
0
0
Categories in category theory
Fukaya category
0
0
0
Categories in category theory
Functor category
0
0
0
Categories in category theory
Kleisli category
0
0
0
Categories in category theory
Monoid (category theory)
0
0
0
Categories in category theory
Regular category
0
0
0
Categories in category theory
Small set (category theory)
0
0
0
Categories in category theory
Category theorists
0
0
0
Category theory
André Joyal
0
0
0
Category theorists
Andrée Ehresmann
0
0
0
Category theorists
Charles Ehresmann
0
0
0
Category theorists
Charles Rezk
0
0
0
Category theorists
David Spivak
0
0
0
Category theorists
Emily Riehl
0
0
0
Category theorists
Eugenia Cheng
0
0
0
Category theorists
Jacob Lurie
0
0
0
Category theorists
Jacques Feldbau
0
0
0
Category theorists
Jacques Riguet
0
0
0
Category theorists
Jean Bénabou
0
0
0
Category theorists
John C. Baez
0
1
0
Category theorists
John C. Oxtoby
0
0
0
Category theorists
John R. Isbell
0
0
0
Category theorists
Kenneth Brown (mathematician)
0
0
0
Category theorists
Martin Hyland
0
0
0
Category theorists
Max Kelly
0
0
0
Category theorists
Michael Barr (mathematician)
0
0
0
Category theorists
Michael Shulman (mathematician)
0
0
0
Category theorists
Myles Tierney
0
0
0
Category theorists
Peter J. Freyd
0
0
0
Category theorists
Peter Johnstone (mathematician)
0
0
0
Category theorists
Richard J. Wood
0
0
0
Category theorists
Ross Street
0
0
0
Category theorists
Samuel Eilenberg
0
0
0
Category theorists
Urs Schreiber
0
0
0
Category theorists
Valeria de Paiva
0
0
0
Category theorists
Věra Trnková
0
0
0
Category theorists
William Lawvere
0
0
0
Category theorists
Closed categories
0
0
0
Category theory
*-autonomous category
0
0
0
Closed categories
Cartesian closed category
0
0
0
Closed categories
Closed category
0
0
0
Closed categories
Closed monoidal category
0
0
0
Closed categories
Compact closed category
0
0
0
Closed categories
Dagger categories
0
0
0
Category theory
Category of finite-dimensional Hilbert spaces
0
0
0
Dagger categories
Dagger category
0
0
0
Dagger categories
Dagger compact category
0
0
0
Dagger categories
Dagger symmetric monoidal category
0
0
0
Dagger categories
Ribbon category
0
0
0
Dagger categories
Duality theories
0
0
0
Category theory
Adjoint functors
0
0
0
Duality theories
Closure operators
0
0
0
Duality theories
Self-duality
0
0
0
Duality theories
Alvis–Curtis duality
0
0
0
Duality theories
Artin–Verdier duality
0
0
0
Duality theories
Born reciprocity
0
0
0
Duality theories
Convex conjugate
0
0
0
Duality theories
Dual abelian variety
0
0
0
Duality theories
Dual polyhedron
0
0
0
Duality theories
Dual system
0
0
0
Duality theories
Dual wavelet
0
0
0
Duality theories
Duality (electrical circuits)
0
0
0
Duality theories
Duality (electricity and magnetism)
0
0
0
Duality theories
Duality (mathematics)
0
0
0
Duality theories
Duality (mechanical engineering)
0
0
0
Duality theories
Duality (order theory)
0
0
0
Duality theories
Duality (projective geometry)
0
0
0
Duality theories
Esakia duality
0
0
0
Duality theories
Fei–Ranis model of economic growth
0
0
0
Duality theories
Ancestors
(4)
Fields of abstract algebra
Fields of mathematics
Mathematics
Index
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