Library UniMath.Bicategories.MonoidalCategories.PointedFunctorsWhiskeredMonoidal

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Ralph Matthes

2022

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Contents :

build monoidal category in whiskered form for the pointed endofunctors through a displayed monoidal category

Require Import UniMath.Foundations.PartD.
Require Import UniMath.MoreFoundations.All.

Require Import UniMath.CategoryTheory.Core.Categories.
Require Import UniMath.CategoryTheory.Core.Functors.
Require Import UniMath.CategoryTheory.FunctorCategory.
Require Import UniMath.CategoryTheory.whiskering.
Require Import UniMath.CategoryTheory.Core.NaturalTransformations.
Require UniMath.CategoryTheory.PointedFunctors.
Require UniMath.CategoryTheory.PointedFunctorsComposition.
Require Import UniMath.CategoryTheory.Monoidal.Categories.
Require Import UniMath.CategoryTheory.DisplayedCats.Core.
Require Import UniMath.CategoryTheory.DisplayedCats.Total.
Require Import UniMath.CategoryTheory.DisplayedCats.Isos.
Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.
Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors.
Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal.
Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal.
Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects.
Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal.
Require Import UniMath.CategoryTheory.coslicecat.

Import MonoidalNotations.

Local Open Scope cat.

Section A.
Context (C : category).

Definition pointedfunctors_disp_cat : disp_cat (cat_of_endofunctors C)
  := coslice_cat_disp (cat_of_endofunctors C) I_{monoidal_of_endofunctors C }.

Definition pointedfunctors_cat : category := total_category pointedfunctors_disp_cat.
Definition pointedfunctors_disp_moncat : disp_monoidal pointedfunctors_disp_cat
                                                       (monoidal_of_endofunctors C)
  := monoidal_pointed_objects_disp (monoidal_of_endofunctors C).

Definition pointedfunctors_moncat : monoidal pointedfunctors_cat
  := total_monoidal pointedfunctors_disp_moncat.

End A.