nLab invertible object

Definition

Definition

In a monoidal category, a dualizable object $A$ for which the structure unit (and counit) maps between $A \otimes A^\ast$ (and $A^\ast \otimes A$) 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.

Related concepts

• Picard group

• line, line object

• dualizable object

• invertible field theory