proposition: Corollary cofree_comonoid_REL_map_contr : iscontr (∑ f' : commutative_comonoid_category REL_sym_mon_closed_cat ⟦ C, cofree_comonoid_REL X ⟧, f = # (underlying_commutative_comonoid REL_sym_mon_closed_cat) f' · map_to_cofree_comonoid_REL X).
proof: Proof. use iscontraprop1. - apply cofree_comonoid_REL_map_unique. - simple refine (_ ,, _). + exact cofree_comonoid_REL_map. + exact cofree_comonoid_REL_map_comm. Defined.
imports: UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.Algebra.Free_Monoids_and_Groups UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Categories.Rel UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Adjunctions UniMath.CategoryTheory.Monoidal.FunctorCategories UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Monoidal.Displayed.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Monoidal.Comonoids.Category UniMath.CategoryTheory.Monoidal.Comonoids.Monoidal UniMath.CategoryTheory.Monoidal.Comonoids.Symmetric UniMath.CategoryTheory.Monoidal.Comonoids.CommComonoidsCartesian UniMath.CategoryTheory.Monoidal.Examples.Relations UniMath.Semantics.LinearLogic.LafontCategory