nLab
opposite 2-category

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

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