---
date: 2022-02-23 18:45
modification date: Wednesday 23rd February 2022 18:45:08
title: Kan complex
aliases: [Kan complexes, Kan]

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


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- Tags 
	- #higher-algebra 
- Refs:
	- #todo/add-references
- Links:
	- [simplicial set](Unsorted/simplicial%20set.md)
	- [infinity category](Unsorted/infinity%20categories.md)
	- [infty groupoids](Unsorted/homotopy%20type.md)

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# Kan complex

- A [simplicial set](simplicial%20set.md) in which every horn (not just inner) admits a filler.
- Fibrant objects in simplicial sets.

![attachments/Pasted image 20210604002351.png](attachments/Pasted%20image%2020210604002351.png)

![](attachments/Pasted%20image%2020220327014159.png)

![](attachments/Pasted%20image%2020220511003951.png)