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Theorems · Definition · category theory

CategoryTheory.Square.IsPushout

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Square C → Prop

The condition that a commutative square is a pushout square.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square
Cited by
20 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Square.IsPushout.map · cited by 2IsPushout.mapCategoryTheory.Square.IsPushout.mk · cited by 2IsPushout.mkCategoryTheory.Square.IsPushout.of_iso · cited by 2IsPushout.of_isoCategoryTheory.Square.IsPushout.op · cited by 2IsPushout.opCategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushout · cited by 2MayerVietorisSquare.isPus…CategoryTheory.Square.IsPushout.epi_f₂₄ · cited by 1IsPushout.epi_f₂₄CategoryTheory.Square.IsPushout.flip · cited by 1IsPushout.flipCategoryTheory.Square.IsPushout.isColimit · cited by 1IsPushout.isColimitCategoryTheory.Square.IsPushout.isColimitCokernelCofork · cited by 1IsPushout.isColimitCokern…CategoryTheory.Square.IsPushout.of_map · cited by 1IsPushout.of_mapCategoryTheory.Square.isPushout_iff · cited by 1Square.isPushout_iffCategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk.inj · cited by 1mk.injCategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk.noConfusion · cited by 1mk.noConfusionCategoryTheory.GrothendieckTopology.MayerVietorisSquare.isPushoutAddCommGrpFreeSheaf · cited by 1MayerVietorisSquare.isPus…CategoryTheory.Square.IsPullback.op · cited by 0IsPullback.opCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.IsPushout · cited by 219CategoryTheory.IsPushoutCategoryTheory.Square · cited by 193CategoryTheory.SquareCategoryTheory.Square.f₁₃ · cited by 56Square.f₁₃CategoryTheory.Square.f₂₄ · cited by 52Square.f₂₄CategoryTheory.Square.f₁₂ · cited by 51Square.f₁₂CategoryTheory.Square.f₃₄ · cited by 51Square.f₃₄Square.IsPushoutCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by28

Results whose statement or proof uses this declaration.