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Theorems · Definition · algebraic topology

CategoryTheory.SimplicialObject.Splitting.ofIso

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {X Y : CategoryTheory.SimplicialObject C} → X.Splitting → (X ≅ Y) → Y.Splitting

A simplicial object that is isomorphic to a split simplicial object is split.

Defined in
Mathlib.AlgebraicTopology.SimplicialObject.Split
Cited by
2 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

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

CategoryTheory.SimplicialObject.Splitting.ofIso_ι · cited by 0Splitting.ofIso_ιCategoryTheory.SimplicialObject.Splitting.ofIso_N · cited by 0Splitting.ofIso_NCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compOpposite · cited by 8081OppositeCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Iso · cited by 3963CategoryTheory.IsoSimplexCategory · cited by 2204SimplexCategoryCategoryTheory.SimplicialObject · cited by 548CategoryTheory.Simplicial…CategoryTheory.Iso.app · cited by 253Iso.appCategoryTheory.SimplicialObject.Splitting.N · cited by 81Splitting.NCategoryTheory.SimplicialObject.Splitting.IndexSet · cited by 65Splitting.IndexSetCategoryTheory.SimplicialObject.Splitting · cited by 59SimplicialObject.SplittingCategoryTheory.Limits.IsColimit.ofIsoColimit · cited by 45IsColimit.ofIsoColimitCategoryTheory.SimplicialObject.Splitting.ι · cited by 21Splitting.ιCategoryTheory.Limits.Cofan.ext · cited by 6Cofan.extSplitting.ofIsoCITED BYCITES

Cites16

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Cited by2

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