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Theorems · Theorem · category theory

CategoryTheory.Localization.essSurj

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (L : CategoryTheory.Functor C D)
  (W : CategoryTheory.MorphismProperty C) [L.IsLocalization W], L.EssSurj
Defined in
Mathlib.CategoryTheory.Localization.Predicate
Cited by
16 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalization

Around this declaration

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

CategoryTheory.Localization.natTrans_ext · cited by 7Localization.natTrans_extCategoryTheory.Localization.essSurj_mapArrow · cited by 4Localization.essSurj_mapA…CategoryTheory.ObjectProperty.SerreClassLocalization.preservesCokernel · cited by 3SerreClassLocalization.pr…CategoryTheory.ObjectProperty.SerreClassLocalization.preservesKernel · cited by 3SerreClassLocalization.pr…CategoryTheory.LocalizerMorphism.essSurj_of_hasRightResolutions · cited by 2LocalizerMorphism.essSurj…CategoryTheory.Localization.Preadditive.addCommGroup · cited by 2Preadditive.addCommGroupCategoryTheory.Functor.isPointwiseLeftKanExtensionOfIsoOfIsLocalization · cited by 2Functor.isPointwiseLeftKa…CategoryTheory.Localization.functor_additive_iff · cited by 2Localization.functor_addi…CategoryTheory.Functor.isPointwiseRightKanExtensionOfIsoOfIsLocalization · cited by 2Functor.isPointwiseRightK…CategoryTheory.Functor.faithful_of_comp_of_hasLeftCalculusOfFractions · cited by 1Functor.faithful_of_comp_…CategoryTheory.LocalizerMorphism.essSurj_of_hasLeftResolutions · cited by 1LocalizerMorphism.essSurj…CategoryTheory.ObjectProperty.SerreClassLocalization.epi_map_tfae · cited by 1SerreClassLocalization.ep…CategoryTheory.Localization.essSurj_mapComposableArrows_of_hasRightCalculusOfFractions · cited by 1Localization.essSurj_mapC…CategoryTheory.ObjectProperty.SerreClassLocalization.mono_map_tfae · cited by 1SerreClassLocalization.mo…CategoryTheory.Localization.functor_linear_iff · cited by 1Localization.functor_line…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.Equivalence.inverse · cited by 1130Equivalence.inverseCategoryTheory.Iso.symm · cited by 993Iso.symmCategoryTheory.Iso.trans · cited by 566Iso.transCategoryTheory.Equivalence.counitIso · cited by 480Equivalence.counitIsoCategoryTheory.Functor.IsLocalization · cited by 432Functor.IsLocalizationCategoryTheory.Iso.app · cited by 253Iso.appEquiv.invFun · cited by 163Equiv.invFunCategoryTheory.Functor.EssSurj · cited by 88Functor.EssSurjCategoryTheory.Localization.Construction.objEquiv · cited by 5Construction.objEquivCategoryTheory.Localization.equivalenceFromModel · cited by 3Localization.equivalenceF…CategoryTheory.Localization.qCompEquivalenceFromModelFunctorIso · cited by 1Localization.qCompEquival…Localization.essSurjCITED BYCITES

Cites15

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Cited by19

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