Theorems · Theorem · category theory

CategoryTheory.shrinkYonedaMonObjObjEquiv_symm_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C]
  [inst_2 : CategoryTheory.CartesianMonoidalCategory C] {M : CategoryTheory.Mon C} {Y Y' : C} (g : Y' ⟶ Y)
  (f : Y ⟶ M.X),
  CategoryTheory.shrinkYonedaMonObjObjEquiv.symm (CategoryTheory.CategoryStruct.comp g f) =
    (CategoryTheory.ConcreteCategory.hom ((CategoryTheory.shrinkYonedaMon.{w, v, u}.obj M).map g.op))
      (CategoryTheory.shrinkYonedaMonObjObjEquiv.symm f)

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.ShrinkYoneda

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.CartesianMonoidalCategory