Theorems · Definition · algebraic topology
SSet.modelCategoryQuillen.J
CategoryTheory.MorphismProperty SSet
The generating trivial cofibrations: this is the family of morphisms in SSet
which consists of horn inclusions Λ[n, i].ι : Λ[n, i] ⟶ Δ[n] (for positive n).
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Oppositestatement · cited by 8,081
- iSupproof · cited by 2,415
- SimplexCategorystatement · cited by 2,204
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- SSetstatement · cited by 1,283
- SSet.hornproof · cited by 162
- SSet.Subcomplex.ιproof · cited by 136
- CategoryTheory.MorphismProperty.ofHomsproof · cited by 30
Cited by12
Results whose statement or proof uses this declaration.
- SSet.anodyneExtensions_eq_llp_rlpstatement · cited by 4
- SSet.modelCategoryQuillen.horn_ι_mem_Jstatement · cited by 2
- SSet.innerHornInclusions_le_Jstatement and proof · cited by 2
- SSet.modelCategoryQuillen.fibration_iffstatement and proof · cited by 1
- SSet.modelCategoryQuillen.fibrations_eqstatement · cited by 1
- SSet.anodyneExtensions.horn_ιproof · cited by 1
- SSet.fibration_pullbackObjObjπproof · cited by 1
- SSet.modelCategoryQuillen.J_le_monomorphismsstatement and proof · cited by 1
- SSet.innerAnodyneExtensions_leproof · cited by 0
- SSet.anodyneExtensions_eq_retracts_transfiniteCompositionsOfShapestatement and proof · cited by 0
- SSet.KanComplex.iffproof · cited by 0
- SSet.anodyneExtensions_eq_retracts_transfiniteCompositionsstatement and proof · cited by 0