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.

Related pages

• opposite category

• contravariant 2-functor

• 3-category with contravariance

• opposite adjunction

• reverse monoidal category