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Theorems · Theorem · category theory

CompHausLike.preregular

∀ {P : TopCat → Prop} [CompHausLike.HasExplicitPullbacks P],
  (∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y),
      CategoryTheory.EffectiveEpi f → Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)) →
    CategoryTheory.Preregular (CompHausLike P)
Defined in
Mathlib.Topology.Category.CompHausLike.EffectiveEpi
Cited by
19 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompHausLike.HasExplicitPullbacks
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Around this declaration

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

CompHausLike.LocallyConstant.functor · cited by 11LocallyConstant.functorCompHausLike.LocallyConstant.counit · cited by 4LocallyConstant.counitTopCat.toSheafCompHausLike · cited by 4TopCat.toSheafCompHausLikeCompHausLike.LocallyConstant.unit · cited by 3LocallyConstant.unitCompHausLike.LocallyConstantModule.functor · cited by 3LocallyConstantModule.fun…CompHausLike.LocallyConstant.adjunction · cited by 2LocallyConstant.adjunctiontopCatToSheafCompHausLike · cited by 2topCatToSheafCompHausLikeCompHausLike.LocallyConstant.functor_map_hom_app · cited by 1LocallyConstant.functor_m…CompHausLike.LocallyConstant.functor_obj_obj_obj · cited by 1LocallyConstant.functor_o…CompHausLike.LocallyConstant.unitIso · cited by 0LocallyConstant.unitIsoCompHausLike.LocallyConstant.unit_app · cited by 0LocallyConstant.unit_appCompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply · cited by 0LocallyConstantModule.fun…CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply · cited by 0LocallyConstantModule.fun…CompHausLike.LocallyConstantModule.functor_obj_obj_obj_carrier · cited by 0LocallyConstantModule.fun…CompHausLike.LocallyConstant.adjunction_counit · cited by 0LocallyConstant.adjunctio…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierContinuousMap · cited by 2491ContinuousMapTopCat · cited by 1889TopCatCompHausLike.toTop · cited by 258CompHausLike.toTopCompHausLike · cited by 145CompHausLikeCategoryTheory.EffectiveEpi · cited by 86CategoryTheory.EffectiveE…CategoryTheory.Preregular · cited by 52CategoryTheory.PreregularCompHausLike.HasExplicitPullbacks · cited by 20CompHausLike.HasExplicitP…CompHausLike.pullback · cited by 13CompHausLike.pullbackCompHausLike.pullback.fst · cited by 7pullback.fstCompHausLike.pullback.snd · cited by 7pullback.sndCompHausLike.effectiveEpiStruct · cited by 5CompHausLike.effectiveEpi…CompHausLike.preregularCITED BYCITES

Cites16

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Cited by29

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