Theorems · Theorem · algebraic topology
CategoryTheory.SimplicialObject.Splitting.fromNondegComplex_f_assoc
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X : CategoryTheory.SimplicialObject C} (s : X.Splitting)
[inst_1 : CategoryTheory.Preadditive C] (n : ℕ) {Z : C}
(h : (AlgebraicTopology.AlternatingFaceMapComplex.obj X).X n ⟶ Z),
CategoryTheory.CategoryStruct.comp (s.fromNondegComplex.f n) h =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CategoryStruct.comp (s.ι n) (AlgebraicTopology.DoldKan.PInfty.f n)) h- Cited by
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- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- Oppositestatement · cited by 8,081
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- SimplexCategorystatement · cited by 2,204
- HomologicalComplex.Xstatement · cited by 1,839
- HomologicalComplex.Hom.fstatement · cited by 845
- ComplexShape.downstatement · cited by 605
- CategoryTheory.SimplicialObjectstatement and proof · cited by 548
- AlgebraicTopology.AlternatingFaceMapComplex.objstatement · cited by 146
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