Theorems · Definition · category theory

HomotopyCategory.Plus.subcategoryAcyclic

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Abelian C] → CategoryTheory.ObjectProperty (HomotopyCategory.Plus C)

The property of objects in HomotopyCategory.Plus C that is satisfied by acyclic complexes.

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Plus
Cited by: 1 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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Cites10

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
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CategoryTheory.ObjectPropertystatement · cited by 798
HomotopyCategorystatement · cited by 132
CategoryTheory.ObjectProperty.inverseImageproof · cited by 19
HomotopyCategory.subcategoryAcyclicproof · cited by 10
HomotopyCategory.plusstatement · cited by 9
HomotopyCategory.Plusstatement · cited by 8
HomotopyCategory.Plus.ιproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

HomotopyCategory.Plus.quasiIso_eq_subcategoryAcyclic_trWstatement and proof · cited by 0