Theorems · Definition · category theory

CategoryTheory.HasProjectiveDimensionLE

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Abelian C] → C → ℕ → Prop

An object X in an abelian category has projective dimension ≤ n if all Ext X Y i vanish when n + 1 ≤ i

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Dimension

Cited by

13 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian