---
date: 2022-04-05 23:42
modification date: Tuesday 5th April 2022 23:42:25
title: "dualizable object of a category"
aliases: [dualizable object of a category, dual, duals, dualizable]
---

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

---

- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [fully dualizable](fully%20dualizable.md)

---

# dualizable object of a category

![](attachments/Pasted%20image%2020220510234431.png)


For $(X, \tensor, \one)$ a [Monoidal category](Monoidal%20category.md), right duals: existence of two morphisms
\[
\eps: X\dual \tensor X &\to \one &&\text{evaluation} \\
\eta: \one &\to X\tensor X\dual &&\text{coevaluation}
,\]
along with some diagram.

Objects admitting a left and right dual admit a [trace](trace)