Theorems · Definition · category theory

CategoryTheory.GlueData.mapGlueData

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v, u₁} C] →
    {C' : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v, u₂} C'] →
        (D : CategoryTheory.GlueData C) →
          (F : CategoryTheory.Functor C C') →
            [∀ (i j k : D.J),
                  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan (D.f i j) (D.f i k)) F] →
              CategoryTheory.GlueData C'

A functor that preserves the pullbacks of f i j and f i k can map a family of glue data.

Defined in

Mathlib.CategoryTheory.GlueData

Cited by

24 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimit