fact: Definition AddEquiv (A1 A2 : CategoryWithAdditiveStructure) : UU := ∑ D : (∑ F : (AdditiveFunctor A1 A2 × AdditiveFunctor A2 A1), are_adjoints (dirprod_pr1 F) (dirprod_pr2 F)), (∏ a : A1, is_z_isomorphism (unit_from_left_adjoint (pr2 D) a)) × (∏ b : A2, is_z_isomorphism (counit_from_left_adjoint (pr2 D) b)).
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.BinDirectSums