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Theorems · Definition · category theory

CategoryTheory.Adhesive.isColimitBinaryCofan

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Adhesive C] →
      {X : C} →
        (a b : CategoryTheory.Subobject X) →
          CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.BinaryCofan.mk ⋯.hom ⋯.hom)

Given an object X of an adhesive category C, the coproduct of two subobjects of X is their pushout in C over their pullback.

Defined in
Mathlib.CategoryTheory.Adhesive.Subobject
Cited by
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Foundations
Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Adhesive
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CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.Limits.IsColimit · cited by 773Limits.IsColimitCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Subobject · cited by 385CategoryTheory.SubobjectCategoryTheory.Limits.pushout · cited by 284Limits.pushoutCategoryTheory.Subobject.underlying · cited by 211Subobject.underlyingCategoryTheory.Limits.pushout.inr · cited by 193pushout.inrCategoryTheory.Limits.pushout.inl · cited by 192pushout.inlCategoryTheory.Subobject.arrow · cited by 175Subobject.arrowAdhesive.isColimitBinaryCofanCITED BYCITES

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