nLab
identity function
Contents
Context
Equality and Equivalence
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
-
gauge equivalence
-
Examples.
principle of equivalence
equation
-
fiber product, pullback
-
homotopy pullback
-
Examples.
-
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
Contents
Definition
Given a set , the identity function on is the function that maps any element of to itself:
or equivalently,
The identity functions are the identity morphisms in the category Set of sets.
More generally, in any concrete category, the identity morphism of each object is given by the identity function on its underlying set.
Last revised on December 1, 2019 at 08:20:27.
See the history of this page for a list of all contributions to it.