Theorems · Theorem · category theory

HomologicalComplex.isZero_iff_isStrictlySupported_and_isStrictlySupportedOutside

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (K : HomologicalComplex C c') (e : c.Embedding c'),
  CategoryTheory.Limits.IsZero K ↔ K.IsStrictlySupported e ∧ K.IsStrictlySupportedOutside e

Defined in

Mathlib.Algebra.Homology.Embedding.IsSupported

Cited by

1 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms