---
date: 2022-03-26 20:37
modification date: Saturday 26th March 2022 20:37:52
title: "Ind objects"
aliases: [Ind-objects, Ind-objects, Ind scheme, Ind schemes, Pro object, pro scheme]

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


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- Tags 
	- #higher-algebra 
- Refs:
	- #todo/add-references
- Links:
	- [kappa filtered](kappa%20filtered)

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# Ind objects

$\Ind(\cat C)$ is the category of formal [filtered colimits](filtered%20colimits) ("inductive systems") of objects in $\cat C$.
How to do this: take the [free cocompletion](free%20cocompletion.md) $\cat C \to [\cat C, \Set]$ and compute the colimit there.

![](attachments/Pasted%20image%2020210630222723.png)

# Pro objects

$\Pro\cat C$ is the category of formal limits ("projective systems") of objects in $\cat C$.
Take the free completion $\cat C \to \opcat{ [\cat C, \Set] }$