Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.CodescendsAlong
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
CategoryTheory.MorphismProperty C → CategoryTheory.MorphismProperty C → PropP codescends along Q if whenever Q holds for Z ⟶ X,
P holds for X ⟶ X ∐[Z] Y implies P holds for Z ⟶ Y.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.of_isPushout_of_codescendsAlongstatement and proof · cited by 3
- CategoryTheory.MorphismProperty.CodescendsAlong.of_isPushoutstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.iff_of_isPushoutstatement and proof · cited by 2
- CategoryTheory.MorphismProperty.pushout_inl_iffstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.pushout_inr_iffstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.of_pushout_inl_of_codescendsAlongstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.of_pushout_inr_of_descendsAlongstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.CodescendsAlong.casesOnstatement and proof · cited by 0
- CategoryTheory.MorphismProperty.CodescendsAlong.mk'statement · cited by 0
- CategoryTheory.MorphismProperty.CodescendsAlong.of_lestatement and proof · cited by 0
- CategoryTheory.MorphismProperty.CodescendsAlong.recOnstatement and proof · cited by 0