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.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
- Top.topstatement · cited by 9,680
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- TopCatstatement · cited by 1,889
- ComplexShapestatement and proof · cited by 1,684
- TopPairstatement · cited by 67
- TopCat.isEmbeddingstatement · cited by 67
Cited by26
Results whose statement or proof uses this declaration.
- TopPair.HomologyPretheory.Hom.iso_commstatement · cited by 3
- TopPair.HomologyPretheory.inv_hom_iso_homₚstatement and proof · cited by 2
- TopPair.HomologyPretheory.iso_homₚ_inv_homstatement and proof · cited by 2
- TopPair.HomologyPretheory.Hom.extproof · cited by 1
- TopPair.HomologyPretheory.Hom.iso_comm_appstatement · cited by 1
- TopPair.HomologyPretheory.Hom.iso_comm_assocstatement and proof · cited by 1
- TopPair.HomologyPretheory.Hom.mk.injstatement and proof · cited by 1
- TopPair.HomologyPretheory.extstatement and proof · cited by 1
- TopPair.HomologyPretheory.Hom.mk.noConfusionstatement and proof · cited by 1
- TopPair.HomologyPretheory.inv_hom_iso_homₚ_appstatement · cited by 1
- TopPair.HomologyPretheory.iso_homₚ_inv_hom_appstatement · cited by 1
- TopPair.HomologyPretheory.Hom.casesOnstatement and proof · cited by 0