---
date: 2022-04-05 23:42
modification date: Tuesday 5th April 2022 23:42:25
title: "linear category"
aliases: [linear category]
created: 2023-03-31T14:42
updated: 2023-03-31T14:43
---

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

---
- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [idemptotent-1complete category](idemptotent-complete%20category)
	- [Mackey functor](Mackey%20functor)
	- [smooth category](smooth%20category.md)

---

# linear category


- A category [Enriched](Enriched) over $(\kmod, \tensor_k])$.
	- So hom sets are $k\dash$modules and composition is bilinear.
- More generally, a category is $R\dash$linear if it is enriched over $(\rmod, \tensor_R)$. 

![](2023-03-31-33.png)
  
![](attachments/Pasted%20image%2020220410003226.png)

![](attachments/Pasted%20image%2020220510160802.png)