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identity morphism

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  • Morphism — In mathematics, a morphism is an abstraction derived from structure preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear… …   Wikipedia

  • Identity function — In mathematics, an identity function, also called identity map or identity transformation, is a function that always returns the same value that was used as its argument. In terms of equations, the function is given by f ( x ) = x… …   Wikipedia

  • Zero morphism — In category theory, a zero morphism is a special kind of morphism exhibiting properties like those to and from a zero object. Suppose C is a category, and f : X → Y is a morphism in C. The morphism f is called a constant morphism (or… …   Wikipedia

  • Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… …   Wikipedia

  • Category (mathematics) — In mathematics, a category is an algebraic structure that comprises objects that are linked by arrows . A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A …   Wikipedia

  • Comma category — In mathematics, a comma category (a special case being a slice category) is a construction in category theory. It provides another way of looking at morphisms: instead of simply relating objects of a category to one another, morphisms become… …   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

  • Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   Wikipedia

  • Glossary of category theory — This is a glossary of properties and concepts in category theory in mathematics.CategoriesA category A is said to be: * small provided that the class of all morphisms is a set (i.e., not a proper class); otherwise large. * locally small provided… …   Wikipedia

  • Enriched category — In category theory and its applications to mathematics, an enriched category is a category whose hom sets are replaced by objects from some other category, in a well behaved manner.DefinitionWe define here what it means for C to be an enriched… …   Wikipedia

  • Multicategory — In mathematics (especially category theory), a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are viewed as analogous to functions, then morphisms in a… …   Wikipedia

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