Coherence Of Involutive Categories

In this chapter, we present the definitions and basic properties of involutive categories, involutive functors, involutive natural transformations, involutive adjunctions, and involutive objects in involutive categories. An important observation is Theorem 2.3.8, which says that an adjoint of an involutive functor must also be an involutive functor such that the adjunction is an involutive adjunction. As a consequence, an involutive functor that is also an equivalence of categories is automatically an involutive equivalence.