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Theorems · Definition · category theory

CategoryTheory.Limits.pushout.inr

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      (f : X ⟶ Y) →
        (g : X ⟶ Z) → [inst_1 : CategoryTheory.Limits.HasPushout f g] → Z ⟶ CategoryTheory.Limits.pushout f g

The second inclusion into the pushout of f and g.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback
Cited by
193 results in Mathlib
Foundations
Depth 24 from the axioms, rests on 150 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasPushout

Around this declaration

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

CategoryTheory.Functor.PushoutObjObj.ofHasPushout · cited by 34PushoutObjObj.ofHasPushoutCategoryTheory.Limits.pushout.hom_ext · cited by 30pushout.hom_extCategoryTheory.Limits.pushout.condition · cited by 23pushout.conditionCategoryTheory.Under.pushout · cited by 21Under.pushoutCategoryTheory.IsPushout.of_hasPushout · cited by 20IsPushout.of_hasPushoutCategoryTheory.Limits.hasPushout_symmetry · cited by 18Limits.hasPushout_symmetryCategoryTheory.MorphismProperty.Under.pushout · cited by 15Under.pushoutCategoryTheory.Limits.pushout.map · cited by 14pushout.mapCategoryTheory.Limits.pushoutAssoc · cited by 12Limits.pushoutAssocCategoryTheory.Limits.pushoutLeftPushoutInrIso · cited by 12Limits.pushoutLeftPushout…AlgebraicGeometry.Scheme.Pullback.Triplet.tensorInr · cited by 9Triplet.tensorInrCategoryTheory.SmallObject.ρFunctorObj · cited by 9SmallObject.ρFunctorObjCategoryTheory.Limits.pushoutComparison · cited by 8Limits.pushoutComparisonCategoryTheory.IsPushout.inr_isoPushout_hom · cited by 8IsPushout.inr_isoPushout_…CategoryTheory.Limits.inl_comp_pushoutSymmetry_hom_assoc · cited by 8Limits.inl_comp_pushoutSy…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.colimit.ι · cited by 397colimit.ιCategoryTheory.Limits.span · cited by 294Limits.spanCategoryTheory.Limits.pushout · cited by 284Limits.pushoutCategoryTheory.Limits.HasPushout · cited by 192Limits.HasPushoutCategoryTheory.Limits.WalkingSpan.right · cited by 78WalkingSpan.rightpushout.inrCITED BYCITES

Cites7

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

Cited by227

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 227.