Theorems · Inductive type · category theory

CategoryTheory.HasProjectiveDimensionLT

{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 ≤ i. See also HasProjectiveDimensionLE. (Do not use the subsingleton' field directly. Use the constructor HasProjectiveDimensionLT.mk, and the lemmas hasProjectiveDimensionLT_iff and Ext.eq_zero_of_hasProjectiveDimensionLT.)

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Dimension

Cited by

26 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian