nLab
invertible object

Contents

Context

Monoidal categories

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.