fact: Definition free_alg_coproduct (X Y : hSet) : BinCoproduct (monad_free_alg X) (monad_free_alg Y) := (monad_free_alg (setcoprod X Y) ,, _ ,, _) ,, left_adjoint_preserves_bincoproduct (left_adjoint monad_underlying_is_right_adjoint) (is_left_adjoint_left_adjoint _) _ _ _ _ _ (pr2 (BinCoproductsHSET X Y)).
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits UniMath.CategoryTheory.Monads.Monads