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 Category theory
category theory Concepts
identity morphism, or simply identity, of an object in some x x category is the morphism C C , or 1 x : x → x 1_x: x \to x , which acts as a two-sided identity for id x : x → x \id_x: x \to x composition.
small category with set of objects C C and set of morphisms C 0 C_0 , the C 1 C_1 identity assigning function of is the function C C that maps each object in i : C 0 → C 1 i: C_0 \to C_1 to its identity morphism in C 0 C_0 . C 1 C_1
For the generalisation to an
internal category , see C C identity-assigning morphism.
Set, the identity morphisms are the identity functions.
Is there a wide-spread notation for identity morphism on a specified object of a specific category
? (I consider several categories and there are several different identity morphisms (one for each category) on the same object.) C C
Revised on May 20, 2015 17:12:39