Theorems · Theorem

CategoryTheory.Limits.limit.w_apply

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  (F : CategoryTheory.Functor J C) [inst_2 : CategoryTheory.Limits.HasLimit F] {j j' : J} (f : j ⟶ j')
  {F_1 : C → C → Type uF} {carrier : C → Type w} {instFunLike : (X Y : C) → FunLike (F_1 X Y) (carrier X) (carrier Y)}
  [inst_3 : CategoryTheory.ConcreteCategory C F_1] (x : carrier (CategoryTheory.Limits.limit F)),
  (CategoryTheory.ConcreteCategory.hom (F.map f))
      ((CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.limit.π F j)) x) =
    (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.limit.π F j')) x

Defined in

Mathlib.CategoryTheory.ConcreteCategory.Elementwise

Cited by

3 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitCategoryTheory.ConcreteCategory