proposition: Lemma free_monoid_coeq_sequence_converges_gives_adjoint_mon_alg : Mon_alg _ T.
proof: Proof. exists Tinf. use tpair. - set (limit_step := free_monoid_coeq_sequence_limit_ordinal_step_on I_{V}). set (σinfty := pair_diagram_arr limit_step). exact (σinfty · z_iso_inv_from_is_z_iso _ Hconv). - abstract ( apply pathsinv0; use colim_endo_is_identity; intro n; apply pathsinv0; etrans; [exact (pathsinv0 (id_right _))|]; apply cancel_precomposition; apply pathsinv0; etrans; [apply assoc|]; exact (pr12 Hconv) ). Defined.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Chains.Chains UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.ModelCategories.Generated.GenericFreeMonoid UniMath.ModelCategories.Generated.MonoidalHelpers UniMath.ModelCategories.Helpers