nLab
identity functor
Redirected from "identity functors".
Contents
Context
Category theory
Equality and Equivalence
equivalence
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equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
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identity type, equivalence of types, definitional isomorphism
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isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
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natural equivalence, natural isomorphism
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gauge equivalence
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Examples.
principle of equivalence
equation
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fiber product, pullback
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homotopy pullback
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Examples.
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linear equation, differential equation, ordinary differential equation, critical locus
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Euler-Lagrange equation, Einstein equation, wave equation
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Schrödinger equation, Knizhnik-Zamolodchikov equation, Maurer-Cartan equation, quantum master equation, Euler-Arnold equation, Fuchsian equation, Fokker-Planck equation, Lax equation
Contents
Idea
The identity functor on a category is the functor that maps each object and morphism of to itself. The identity functors are the identities for composition of functors in Cat.
Last revised on December 1, 2019 at 08:18:30.
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