nLab
opposite 2-category

A 2-category $K$ has three different opposites:

• 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 $K^{\mathrm{coop}}$ in which both 1-cells and 2-cells are reversed.