# nLab opposite 2-category

## Definition

A 2-category $K$ has three different opposites (two independent):

• The $1$-cell dual $K^{op}$, in which the $1$-cells but not the $2$-cells are reversed.
• The $2$-cell dual $K^{co}$, in which the $2$-cells but not the $1$-cells are reversed.
• The bidual $K^{co op}$ in which both $1$-cells and $2$-cells are reversed.

Revised on June 17, 2016 14:17:03 by Mike Shulman (192.195.154.58)