Equality and Equivalence
equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
identity type, equivalence in homotopy type theory
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
natural equivalence, natural isomorphism
principle of equivalence
fiber product, pullback
linear equation, differential equation, ordinary differential equation, critical locus
Euler-Lagrange equation, Einstein equation, wave equation
Schrödinger equation, Knizhnik-Zamolodchikov equation, Maurer-Cartan equation, quantum master equation, Euler-Arnold equation, Fuchsian equation, Fokker-Planck equation, Lax equation
The identity morphism, or simply identity, of an object in some category is the morphism , or , which acts as a two-sided identity for composition.
Given a small category with set of objects and set of morphisms , the identity assigning function of is the function that maps each object in to its identity morphism in .
For the generalisation to an internal category , see identity-assigning morphism.
In Set, the identity morphisms are the identity functions.
Revised on November 6, 2014 06:44:42
by Urs Schreiber