---
date: 2022-02-23 18:45
modification date: Friday 1st April 2022 12:13:37
title: "Yoneda lemma"
aliases: [Yoneda embedding, Yoneda, representable]

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Last modified date: <%+ tp.file.last_modified_date() %>


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- Tags 
	- #cats 
- Refs:
	- #todo/add-references
- Links:
	- [pointed category](pointed%20category.md)

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# Yoneda lemma

- The Yoneda embedding: the functional functor:
$$
Y: \cat{C} \to \Fun(\cat C, \Set) = \Presh(\cat C, \Set)  \quad
Y(\wait) := \Fun(\wait, \Set) \circ \opcat{(\wait)} \quad
X \mapsto \Hom_{\cat{C} } (\wait, X)
$$
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