Theorems · Theorem · category theory

CategoryTheory.shrinkYonedaGrp_obj_map_shrinkYonedaGrpObjObjEquiv_symm

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C]
  [inst_2 : CategoryTheory.CartesianMonoidalCategory C] {M : CategoryTheory.Grp C} {Y Y' : Cᵒᵖ} (g : Y ⟶ Y')
  (f : Opposite.unop Y ⟶ M.X),
  (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.shrinkYonedaGrp.{w, v, u}.obj M).map g))
      (CategoryTheory.shrinkYonedaGrpObjObjEquiv.symm f) =
    CategoryTheory.shrinkYonedaGrpObjObjEquiv.symm (CategoryTheory.CategoryStruct.comp g.unop f)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.ShrinkYoneda

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.CartesianMonoidalCategory