# nLab natural equivalence

### Context

#### 2-Category theory

2-category theory

## Definitions

• 2-category

• strict 2-category

• bicategory

• enriched bicategory

• ## Transfors between 2-categories

• 2-functor

• 2-natural transformation

• modification

• Yoneda lemma for bicategories

• ## Morphisms in 2-categories

• fully faithful morphism

• faithful morphism

• conservative morphism

• pseudomonic morphism

• discrete morphism

• eso morphism

• ## Structures in 2-categories

• mate

• cartesian object

• fibration in a 2-category

• codiscrete cofibration

• ## Limits in 2-categories

• 2-limit

• 2-pullback

• comma object

• inserter

• inverter

• equifier

• ## Structures on 2-categories

• monoidal 2-category

• Gray tensor product

• proarrow equipment

• #### Higher category theory

higher category theory

# 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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Last revised on November 20, 2012 at 21:41:05. See the history of this page for a list of all contributions to it.