Theorems · Theorem · algebraic topology
SSet.relativeCellComplexOfMono_isColimit
∀ {X Y : SSet} (i : X ⟶ Y) [inst : CategoryTheory.Mono i],
(SSet.relativeCellComplexOfMono i).isColimit =
(CategoryTheory.Limits.isColimitOfPreserves SSet.Subcomplex.toSSetFunctor
(CategoryTheory.Limits.CompleteLattice.colimitCocone ⋯.functor).isColimit).ofIsoColimit
(CategoryTheory.Limits.Cocone.ext (SSet.Subcomplex.eqToIso ⋯ ≪≫ SSet.Subcomplex.topIso Y) ⋯)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Mono
Around this declaration
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Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement · cited by 16,252
- Top.topstatement · cited by 9,680
- Oppositestatement · cited by 8,081
- CategoryTheory.Functor.compstatement · cited by 6,529
- SimplexCategorystatement · cited by 2,204
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- SSetstatement and proof · cited by 1,283
- CategoryTheory.Functor.conststatement · cited by 1,264
- OrderHomstatement · cited by 934
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