Theorems · Definition · category theory

CategoryTheory.Limits.LimitPresentation.map

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : Type w} →
      [inst_1 : CategoryTheory.Category.{t, w} J] →
        {X : C} →
          CategoryTheory.Limits.LimitPresentation J X →
            {D : Type u_1} →
              [inst_2 : CategoryTheory.Category.{v_1, u_1} D] →
                (F : CategoryTheory.Functor C D) →
                  [CategoryTheory.Limits.PreservesLimitsOfShape J F] →
                    CategoryTheory.Limits.LimitPresentation J (F.obj X)

If F preserves limits of shape J, it maps limit presentations of X to limit presentations of F(X).

Defined in

Mathlib.CategoryTheory.Limits.Presentation

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimitsOfShape