Theorems · Definition · category theory

CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.iso

{C : Type u} →
  [inst : CategoryTheory.SmallCategory C] →
    [inst_1 : CategoryTheory.Limits.HasFiniteColimits C] →
      (A : CategoryTheory.Functor Cᵒᵖ (Type u)) →
        {J : Type} →
          [inst_2 : CategoryTheory.SmallCategory J] →
            [inst_3 : CategoryTheory.FinCategory J] →
              (K : CategoryTheory.Functor J Cᵒᵖ) →
                [CategoryTheory.IsFiltered (CategoryTheory.CostructuredArrow CategoryTheory.yoneda A)] →
                  A.obj (CategoryTheory.Limits.limit K) ≅ CategoryTheory.Limits.limit (K.comp A)

(Implementation) The isomorphism that proves that A preserves finite limits.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Presheaf

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.SmallCategoryCategoryTheory.Limits.HasFiniteColimitsCategoryTheory.SmallCategoryCategoryTheory.FinCategoryCategoryTheory.IsFiltered