fact: Definition free_monoid_theory_algebra_to_unit (A : algebra free_monoid_theory) : A := action unit_el (weqvecfun _ [()]).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Algebra.BinaryOperations UniMath.Algebra.Free_Monoids_and_Groups UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Categories.Monoid UniMath.Combinatorics.Lists UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.AlgebraicTheories.AlgebraicTheoryCategoryCore UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.Algebras UniMath.AlgebraicTheories.AlgebraCategoryCore UniMath.AlgebraicTheories.AlgebraCategory UniMath.AlgebraicTheories.AlgebraMorphisms UniMath.AlgebraicTheories.Examples.FreeObjectTheory