Theorems · Inductive type · category theory

CategoryTheory.HasInjectiveDimensionLT

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

An object X in an abelian category has Injective dimension < n if all Ext X Y i vanish when n ≤ i. See also HasInjectiveDimensionLE. (Do not use the subsingleton' field directly. Use the constructor HasInjectiveDimensionLT.mk, and the lemmas hasInjectiveDimensionLT_iff and Ext.eq_zero_of_hasInjectiveDimensionLT.)

Defined in

Mathlib.CategoryTheory.Abelian.Injective.Dimension

Cited by

23 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian