nLab
star-category

**-categories

Idea

The notion of **-category combines that of a \dagger-category and of an \mathbb{C}-algebroid (i.e. a \mathbb{C}-linear category). Thus it might reasonably be called simply a \mathbb{C}-linear \dagger-category. However, **-categories were popular in AQFT for a while, while the notion of dagger-category was introduced in the context of quantum information theory, so for historical reasons we have two names.

Definition

Definition

A **-category is a category that is a \dagger-category and a \mathbb{C}-algebroid such that the dagger operation is conjugate linear.

In a **-category, the dagger operation \dagger is synonymously denoted **.

Examples

See DHR category.

Revised on April 5, 2013 13:12:05 by Urs Schreiber (82.169.65.155)