index of category theory
- category theory
- object
- identity
- arrow
- morphism
- composition law
- commutativity
- associativity
- axioms of category theory
- ETAC
- triples
- Abelian group
- group
- groupoid
- semigroup
- monoid
- ring
- diagram
- precategory
- category
- alternative definition of category
- subcategory
- small category
- category of sets (
,
)
- automorphism
- commutative diagram
- concrete category
- dual category
- duality principle
- endomorphism
- epi
- monic
- extremal monomorphism
- source
- sink
- initial source
- final sink
- isomorphism-closed subcategory
- locally finite category
- preimage of category
- product of categories
- types
of morphisms
- wellpowered category
- zero object
-small
- equalizer
- subobject
- quotient object
- direct product
- direct sum
- pullback
- pushout
- direct limit
- limiting cone
- cocone and colimit functor
- complete category
- groupoid (category theoretic)
- functor
- autofunctor
- category isomorphism
- diagonal functor
- endofunctor
- forgetful functor
- identity functor
- isomorphism
- multifunctor
- natural transformation
- surjective
maps
- univalent functors
- faithful functor
- full functor
- natural equivalence
- adjoint functor
- equivalence of categories
- isomorphic categories
- universal property
- representable functor
- Equivalent definition of a Representable Functor
- simplicial
object
- Yoneda-Grothendieck lemma
- properties of monomorphisms and epimorphisms
- properties of regular
and extremal monomorphisms
- monomorphisms are pullback stable
- proof that an equalizer is a monomorphism
- categorical direct product is an inverse limit
- kernel is an inverse limit
- discrete category
- category example (arrow category)
- category of sets
- category of Abelian groups
- category of topological
spaces
- category of pointed topological spaces
- simplicial category
- category of groupoids
- category associated to a partial order
- category of matrices
- Category of pseudomorphisms
- Category of intermorphisms
- examples of initial objects and terminal objects and zero objects
- monoid as a category
- comma category
- enriched category
- algebraic category
- Logic category
- quantum logic
category
- quantum topos
- algebra formed from a category
- monad
- comonad
- monoidal category
- group object
- nerve
- gerbs
- preadditive category
- additive category
- abelian category
- supplemental axioms for an Abelian category
- exact sequence
- exact functor
- Grothendieck spectral sequence
- enough projectives
- enough injectives
- projective object
- injective object
- derived functor
- derived category
- algebraic K-theory
- examples of algebraic K-theory groups
- Grothendieck group
- delta functor
- horseshoe lemma
- syzygy
- Ext
- Tor
- projective dimension
- 5-lemma
- proof of 5-lemma
- 9-lemma
- snake lemma
- proof of snake lemma
- chain homotopy
- chain homotopy equivalence
- chain map
- homology of a chain complex
- Leray spectral sequence
- spectral sequence
- presheaf
- sheaf
- sheafification
- presheaf of a topological basis
- stalk
- Étalé space
- resolution of a sheaf
- site
- small site on a scheme
- topos
- cosmos
- Heyting logic algebra
- subobject classifier
- well-pointed topos
- power
object
- exponential object
- Cartesian closed category
- natural numbers object
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