Theorems · Theorem · category theory
CategoryTheory.projectiveDimension_lt_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {X : C} {n : ℕ},
CategoryTheory.projectiveDimension X < ↑n ↔ CategoryTheory.HasProjectiveDimensionLT X n- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- Bot.botproof · cited by 4,720
- Nat.cast_oneproof · cited by 2,501
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- WithBotstatement and proof · cited by 1,498
- Nat.cast_addproof · cited by 586
- CategoryTheory.HasProjectiveDimensionLTstatement and proof · cited by 26
- CategoryTheory.projectiveDimensionstatement and proof · cited by 19
- csInf_memproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.projectiveDimension_eq_bot_iffproof · cited by 1
- CategoryTheory.projectiveDimension_ge_iffproof · cited by 0