Theorems · Definition · algebraic topology
SSet.RelativeMorphism.botEquiv
{X Y : SSet} → SSet.RelativeMorphism ⊥ ⊥ (SSet.Subcomplex.isInitialBot.to ⊥.toSSet) ≃ (X ⟶ Y)Morphisms relatively to the ⊥ subcomplexes of X and Y
identify to morphisms X ⟶ Y.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- Equivstatement · cited by 8,337
- Oppositestatement · cited by 8,081
- Bot.botstatement and proof · cited by 4,720
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement · cited by 461
- SSet.Subcomplex.toSSetstatement and proof · cited by 315
- CategoryTheory.Limits.IsInitial.tostatement and proof · cited by 119
- SSet.RelativeMorphism.mapproof · cited by 51
- SSet.RelativeMorphismstatement and proof · cited by 39
- SSet.Subcomplex.isInitialBotstatement and proof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- SSet.Homotopyproof · cited by 6
- SSet.Homotopy.h₁statement · cited by 1
- SSet.Homotopy.h₀statement · cited by 1
- SSet.RelativeMorphism.botEquiv_symm_apply_mapstatement and proof · cited by 0
- SSet.Homotopy.h₀_assocstatement · cited by 0
- SSet.RelativeMorphism.botEquiv_applystatement and proof · cited by 0
- SSet.Homotopy.h₁_assocstatement · cited by 0