nLab
identity functor
Contents
Context
Category theory
category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
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

EulerLagrange equation, Einstein equation, wave equation

Schrödinger equation, KnizhnikZamolodchikov equation, MaurerCartan equation, quantum master equation, EulerArnold equation, Fuchsian equation, FokkerPlanck equation, Lax equation
Contents
Idea
The identity functor on a category $C$ is the functor $id_C: C \to C$ that maps each object and morphism of $C$ to itself. The identity functors are the identities for composition of functors in Cat.
Last revised on December 1, 2019 at 03:18:30.
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