nLab
identity natural transformation
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

EulerLagrange equation, Einstein equation, wave equation

Schrödinger equation, KnizhnikZamolodchikov equation, MaurerCartan equation, quantum master equation, EulerArnold equation, Fuchsian equation, FokkerPlanck equation, Lax equation
Category theory
category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
Contents
Definition
The identity natural transformation on a functor $F: C \to D$ is the natural transformation $id_F: F \to F$ that maps each object $x$ of $C$ to the identity morphism $id_{F(x)}$ in $D$.
The identity natural transformations are themselves the identity morphisms for vertical composition of natural transformations in the functor category $D^C$ and in the 2category Cat.
Last revised on December 1, 2019 at 04:13:54.
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