Theorems · Definition · algebraic topology
SSet.Subcomplex.toImage
{X Y : SSet} → (A : X.Subcomplex) → (f : X ⟶ Y) → A.toSSet ⟶ (A.image f).toSSetGiven a morphism of simplicial sets f : X ⟶ Y and a subcomplex A of X,
this is the induced morphism from A to A.image f.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- SSet.Subcomplex.toSSetstatement · cited by 315
- SSet.Subcomplex.ιproof · cited by 136
- SSet.Subcomplex.imagestatement · cited by 26
- SSet.Subcomplex.liftproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.toImage_ιstatement · cited by 1
- SSet.Subcomplex.toImage_app_hom_apply_coestatement and proof · cited by 0
- SSet.Subcomplex.toImage_ι_assocstatement and proof · cited by 0