nLab
natural equivalence

Context

Equality and Equivalence

2-Category theory

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Definition

Often, by a natural equivalence is meant specifically an equivalence in a 2-category of 2-functors.

But more generally it is an equivalence between any kind of functors in higher category theory:

The components of a natural equivalence are equivalences between the objects in the codomain of the functors. This is what the term “natural equivalence” refers to: its a collection of equivalences between objects which are compatible (“natural”) with the morphisms between these objects, and higher morphisms between those.

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Revised on November 20, 2012 21:41:05 by Toby Bartels (64.89.53.83)