nLab
invertible object

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Duality

Contents

Definition

Definition

In a monoidal category, a dualizable object AA for which the structure unit (and counit) maps between AA *A \otimes A^\ast (and A *AA^\ast \otimes A) and the unit object are isomorphisms is called an invertible object.

Remark

A monoidal category in which all objects are invertible is called a 2-group.

Definition

In terms of linear type theory one might speak of invertible types.

Last revised on May 22, 2017 at 14:37:30. See the history of this page for a list of all contributions to it.