18 relations: Algebraic theory, Bicategory, Category (mathematics), Category of small categories, Category theory, Charles Ehresmann, Enriched category, Functor, Higher category theory, Initial and terminal objects, Jonathan Mock Beck, Monoidal category, Morphism, Operad theory, Presheaf (category theory), Product category, Topos, William Lawvere.

## Algebraic theory

Informally in mathematical logic, an algebraic theory is one that uses axioms stated entirely in terms of equations between terms with free variables.

New!!: Strict 2-category and Algebraic theory · See more »

## Bicategory

In mathematics, a bicategory (or a weak 2-category) is a concept in category theory used to extend the notion of category to handle the cases where the composition of morphisms is not (strictly) associative, but only associative up to an isomorphism.

New!!: Strict 2-category and Bicategory · See more »

## Category (mathematics)

In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.

New!!: Strict 2-category and Category (mathematics) · See more »

## Category of small categories

In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories.

New!!: Strict 2-category and Category of small categories · See more »

## Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

New!!: Strict 2-category and Category theory · See more »

## Charles Ehresmann

Charles Ehresmann (19 April 1905 – 22 September 1979) was a French mathematician who worked in differential topology and category theory.

New!!: Strict 2-category and Charles Ehresmann · See more »

## Enriched category

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal category.

New!!: Strict 2-category and Enriched category · See more »

## Functor

In mathematics, a functor is a map between categories.

New!!: Strict 2-category and Functor · See more »

## Higher category theory

In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities.

New!!: Strict 2-category and Higher category theory · See more »

## Initial and terminal objects

In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.

New!!: Strict 2-category and Initial and terminal objects · See more »

## Jonathan Mock Beck

Jonathan Mock Beck (aka Jon Beck; 11 November 1935 – 11 March 2006, Somerville, Massachusetts) was an American mathematician, who worked on category theory and algebraic topology.

New!!: Strict 2-category and Jonathan Mock Beck · See more »

## Monoidal category

In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.

New!!: Strict 2-category and Monoidal category · See more »

## Morphism

In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.

New!!: Strict 2-category and Morphism · See more »

## Operad theory

Operad theory is a field of abstract algebra concerned with prototypical algebras that model properties such as commutativity or anticommutativity as well as various amounts of associativity.

New!!: Strict 2-category and Operad theory · See more »

## Presheaf (category theory)

In category theory, a branch of mathematics, a presheaf on a category C is a functor F\colon C^\mathrm\to\mathbf.

New!!: Strict 2-category and Presheaf (category theory) · See more »

## Product category

In the mathematical field of category theory, the product of two categories C and D, denoted and called a product category, is an extension of the concept of the Cartesian product of two sets.

New!!: Strict 2-category and Product category · See more »

## Topos

In mathematics, a topos (plural topoi or, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site).

New!!: Strict 2-category and Topos · See more »

## William Lawvere

Francis William Lawvere (born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.

New!!: Strict 2-category and William Lawvere · See more »

## Redirects here:

2 category, 2-categorical, 2-categories, 2-category, 2-morphism, 2category, Doctrine (mathematics).