Theorems · Definition · category theory

CategoryTheory.GlueData.gluedIso

{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') →
            [inst_2 : CategoryTheory.Limits.HasMulticoequalizer D.diagram] →
              [inst_3 : CategoryTheory.Limits.PreservesColimit D.diagram.multispan F] →
                [inst_4 :
                    ∀ (i j k : D.J),
                      CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan (D.f i j) (D.f i k)) F] →
                  F.obj D.glued ≅ (D.mapGlueData F).glued

If F preserves the gluing, we obtain an iso between the glued objects.

Defined in

Mathlib.CategoryTheory.GlueData

Cited by

9 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasMulticoequalizerCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.PreservesLimit