Theorems · Theorem · category theory

CategoryTheory.Limits.limit.map_pre

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {K : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} K]
  {C : Type u} [inst_2 : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor J C}
  [inst_3 : CategoryTheory.Limits.HasLimitsOfShape J C] {G : CategoryTheory.Functor J C} (α : F ⟶ G)
  [inst_4 : CategoryTheory.Limits.HasLimitsOfShape K C] (E : CategoryTheory.Functor K J),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.lim.map α) (CategoryTheory.Limits.limit.pre G E) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.limit.pre F E)
      (CategoryTheory.Limits.lim.map (E.whiskerLeft α))

Defined in

Mathlib.CategoryTheory.Limits.HasLimits

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Limits.HasLimitsOfShape