List of category theory topics

List of category theory topics

This is a list of category theory topics, by Wikipedia page.

Specific categories

*Category of sets
**Concrete category
*Category of vector spaces
**Category of graded vector spaces
*Category of finite dimensional Hilbert spaces
*Category of sets and relations
*Category of topological spaces
*Category of metric spaces
*Category of preordered sets
*Category of groups
*Category of abelian groups
*Category of rings
*Category of magmas
*Category of medial magmas

Objects

*Initial object
*Terminal object
*Zero object
*Subobject
*Group object
*Magma object
*Natural number object
*Exponential object

Morphisms

*Epimorphism
*Monomorphism
*Zero morphism
*Normal morphism
*Dual (category theory)
*Groupoid
*Image (category theory)
*Coimage
*Commutative diagram
*Cartesian morphism
*Slice category

Functors

*Isomorphism of categories
*Natural transformation
*Equivalence of categories
*Subcategory
*Faithful functor
*Full functor
*Forgetful functor
*Yoneda lemma
*Representable functor
*Functor category
*Adjoint functors
**Galois connection
**Pontryagin duality
**Affine scheme
*Monad (category theory)
*Comonad
*Combinatorial species
*Exact functor
*Derived functor
*Enriched functor
*Kan extension of a functor
*Hom functor

Limits

*Limit (category theory)
**Product (category theory)
**Equaliser (mathematics)
**Kernel (category theory)
**Pullback (category theory), fiber product
**Inverse limit
***Pro-finite group
*Colimit
**Coproduct
**Coequalizer
**Cokernel
**Pushout (category theory)
**Direct limit
*Biproduct
**Direct sum

Additive structure

*Preadditive category
*Additive category
*Pre-Abelian category
*Abelian category
**Exact sequence
**Exact functor
**Snake lemma
***Nine lemma
**Five lemma
***Short five lemma
**Mitchell's embedding theorem
*Injective cogenerator
*Derived category
*Triangulated category
*Model category
*2-category
*Bicategory

Dagger category

*Dagger symmetric monoidal category
*Dagger compact category
*Strongly ribbon category

Monoidal category

*Closed monoidal category
*Braided monoidal category

Cartesian closed category

Structure (category theory)

*Semigroupoid
*Comma category
*Localization of a category
*Enriched category
*Bicategory

Topoi, toposes

* Topos
* Sheaf
* Gluing axiom
* Descent (category theory)
* Grothendieck topology
* Introduction to topos theory
* Subobject classifier
* Pointless topology
* Heyting algebra

See also: Abstract nonsense, Homological algebra, Glossary of category theory


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • List of group theory topics — Contents 1 Structures and operations 2 Basic properties of groups 2.1 Group homomorphisms 3 Basic types of groups …   Wikipedia

  • List of string theory topics — See also: List of mathematical topics in quantum theory This is an list of string theory topics. Contents 1 String theory 1.1 String duality 1.2 Particles and fields 1 …   Wikipedia

  • List of set theory topics — Logic portal Set theory portal …   Wikipedia

  • Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… …   Wikipedia

  • List of abstract algebra topics — Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this …   Wikipedia

  • List of algebraic topology topics — This is a list of algebraic topology topics, by Wikipedia page. See also: topology glossary List of topology topics List of general topology topics List of geometric topology topics Publications in topology Topological property Contents 1… …   Wikipedia

  • List of algebraic geometry topics — This is a list of algebraic geometry topics, by Wikipedia page. Contents 1 Classical topics in projective geometry 2 Algebraic curves 3 Algebraic surfaces 4 …   Wikipedia

  • List of mathematical logic topics — Clicking on related changes shows a list of most recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes. This is a list of mathematical logic …   Wikipedia

  • List of general topology topics — This is a list of general topology topics, by Wikipedia page. Contents 1 Basic concepts 2 Limits 3 Topological properties 3.1 Compactness and countability …   Wikipedia

  • List of differential geometry topics — This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics. Contents 1 Differential geometry of curves and surfaces 1.1 Differential geometry of curves 1.2 Differential… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”