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Theorems · Definition · category theory

CategoryTheory.Limits.HasMulticoequalizer

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.Limits.MultispanShape} → CategoryTheory.Limits.MultispanIndex J C → Prop

For I : MultispanIndex J C, we say that it has a multicoequalizer if the associated multicospan has a limit.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
Cited by
38 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.GlueData.glued · cited by 44GlueData.gluedCategoryTheory.GlueData.ι · cited by 42GlueData.ιCategoryTheory.Limits.Multicoequalizer.π · cited by 25Multicoequalizer.πCategoryTheory.Limits.HasCoend · cited by 14Limits.HasCoendCategoryTheory.Limits.multicoequalizer · cited by 12Limits.multicoequalizerCategoryTheory.OrthogonalReflection.succ · cited by 11OrthogonalReflection.succCategoryTheory.Limits.Multicoequalizer.desc · cited by 10Multicoequalizer.descCategoryTheory.OrthogonalReflection.fromStep · cited by 9OrthogonalReflection.from…CategoryTheory.GlueData.gluedIso · cited by 9GlueData.gluedIsoCategoryTheory.Limits.Multicoequalizer.hom_ext · cited by 8Multicoequalizer.hom_extCategoryTheory.GlueData.ι_gluedIso_inv · cited by 8GlueData.ι_gluedIso_invCategoryTheory.OrthogonalReflection.toSucc · cited by 7OrthogonalReflection.toSu…CategoryTheory.Limits.Multicoequalizer.sigmaπ · cited by 6Multicoequalizer.sigmaπCategoryTheory.OrthogonalReflection.iteration · cited by 6OrthogonalReflection.iter…CategoryTheory.GlueData.ι_jointly_surjective · cited by 6GlueData.ι_jointly_surjec…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Limits.HasColimit · cited by 307Limits.HasColimitCategoryTheory.Limits.MultispanIndex.multispan · cited by 139MultispanIndex.multispanCategoryTheory.Limits.MultispanIndex · cited by 102Limits.MultispanIndexCategoryTheory.Limits.MultispanShape · cited by 102Limits.MultispanShapeLimits.HasMulticoequalizerCITED BYCITES

Cites5

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

Cited by61

Results whose statement or proof uses this declaration.