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Theorems · Definition · algebraic topology

TopPair.HomologyPretheory.iso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {ι : Type u_2} →
        {c : ComplexShape ι} →
          (self : TopPair.HomologyPretheory C c) → (i : ι) → self.H i ≅ TopPair.incl.comp (self.Hₚ i)

Hₚ and H agree on TopCat.

Defined in
Mathlib.AlgebraicTopology.EilenbergSteenrod
Cited by
21 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

TopPair.HomologyPretheory.Hom.iso_comm · cited by 3Hom.iso_commTopPair.HomologyPretheory.inv_hom_iso_homₚ · cited by 2HomologyPretheory.inv_hom…TopPair.HomologyPretheory.iso_homₚ_inv_hom · cited by 2HomologyPretheory.iso_hom…TopPair.HomologyPretheory.Hom.ext · cited by 1Hom.extTopPair.HomologyPretheory.Hom.iso_comm_app · cited by 1Hom.iso_comm_appTopPair.HomologyPretheory.Hom.iso_comm_assoc · cited by 1Hom.iso_comm_assocTopPair.HomologyPretheory.Hom.mk.inj · cited by 1mk.injTopPair.HomologyPretheory.ext · cited by 1HomologyPretheory.extTopPair.HomologyPretheory.Hom.mk.noConfusion · cited by 1mk.noConfusionTopPair.HomologyPretheory.inv_hom_iso_homₚ_app · cited by 1HomologyPretheory.inv_hom…TopPair.HomologyPretheory.iso_homₚ_inv_hom_app · cited by 1HomologyPretheory.iso_hom…TopPair.HomologyPretheory.Hom.casesOn · cited by 0Hom.casesOnTopPair.HomologyPretheory.Hom.mk.congr_simp · cited by 0mk.congr_simpTopPair.HomologyPretheory.Hom.iso_comm_app_assoc · cited by 0Hom.iso_comm_app_assocTopPair.HomologyPretheory.comp_hom · cited by 0HomologyPretheory.comp_homCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorTop.top · cited by 9680Top.topCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…TopCat · cited by 1889TopCatComplexShape · cited by 1684ComplexShapeTopPair · cited by 67TopPairTopCat.isEmbedding · cited by 67TopCat.isEmbeddingTopPair.HomologyPretheory · cited by 38TopPair.HomologyPretheoryTopPair.HomologyPretheory.Hₚ · cited by 32HomologyPretheory.HₚTopPair.HomologyPretheory.H · cited by 29HomologyPretheory.HHomologyPretheory.isoCITED BYCITES

Cites16

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Cited by26

Results whose statement or proof uses this declaration.