---
date: 2022-04-05 23:42
modification date: Tuesday 5th April 2022 23:42:25
title: "lax functor"
aliases: [lax functor, "lax", "lax monoidal", "lax symmetric monoidal", "op-lax"]
---

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

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

---

# lax functor

![attachments/Pasted image 20210514204948.png](attachments/Pasted%20image%2020210514204948.png)

![attachments/Pasted image 20210514205038.png](attachments/Pasted%20image%2020210514205038.png)

 
 - A lax symmetric monoidal functor $F$ lifts to a functor from commutative [monoid object](monoid%20object.md) in $\cat C$ to commutative monoids in $\cat D$. 

![Pasted image 20211104012535.png](Pasted%20image%2020211104012535.png)