---
date: 2022-12-23 21:37
modification date: Friday 23rd December 2022 21:37:13
title: "Perfect objects"
aliases: [perfect object, perfect objects, perfect]
---

Last modified date: NaN

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [compact object of a category](Unsorted/compact%20object%20of%20a%20category.md)

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# Perfect objects

For $\cat C = \rmod$ and $R$ commutative, perfect = [compact](Unsorted/compact%20object%20of%20a%20category.md) = [dualizable](Unsorted/dualizable.md).
For $\cat C = \Ch(\rmod)$, bounded chain complexes of fg projectives, and compact iff perfect in this category.
For $\cat C = \Ch(\oxmods)$, locally quasi-isomorphic to a bounded complex of free modules of finite type.
Generally, a perfect complex is a compact object in the unbounded derived category $\derivedcat{\rmod}$.