Theorems · Theorem · category theory
CategoryTheory.ComposableArrows.precomp_map
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {n : ℕ} (F : CategoryTheory.ComposableArrows C n) {X : C}
(f : X ⟶ F.left) {X_1 Y : Fin (n + 1 + 1)} (g : X_1 ⟶ Y),
(F.precomp f).map g = CategoryTheory.ComposableArrows.Precomp.map F f X_1 Y ⋯- Cited by
- 4 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.ComposableArrowsstatement and proof · cited by 627
- CategoryTheory.ComposableArrows.leftstatement and proof · cited by 40
- CategoryTheory.ComposableArrows.Precomp.objstatement · cited by 22
- CategoryTheory.ComposableArrows.Precomp.mapstatement · cited by 13
- CategoryTheory.ComposableArrows.precompstatement and proof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.mono_of_mono_of_mono_of_monoproof · cited by 1
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_epiproof · cited by 1
- CategoryTheory.Abelian.isIso_of_epi_of_isIsoproof · cited by 0
- CategoryTheory.Abelian.isIso_of_isIso_of_monoproof · cited by 0