fact: Definition sig_mor : PreCategory := Eval cbv delta [P_associativity P_left_identity P_right_identity] in @sig_mor' A Pmor _ Pidentity Pcompose P_associativity P_left_identity P_right_identity.
imports: HoTT.Tactics Types.Forall Types.Sigma Basics.Trunc Category.Core Functor.Core Category.Sigma.Core Functor.Paths