---
date: 2022-01-15 21:49
modification date: Monday 21st February 2022 00:55:50
title: equivalence of categories
aliases: [equivalence of categories]

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---
date: 2022-04-05 23:42
modification date: Thursday 12th May 2022 16:52:02
title: "equivalence of categories"
aliases: [equivalence of categories]
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- Tags: 
	- #higher-algebra/category-theory 
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# equivalence of categories

A [full](full%20functor) and [faithful](faithful%20functor.md) functor that is [essentially surjective](essentially%20surjective).
Some sources seem to require surjectivity on the underlying isomorphism classes.

![](attachments/Pasted%20image%2020220602202730.png)

# Equivalence vs isomorphism

![](attachments/Pasted%20image%2020220221005612.png)