Theorems · Theorem · category theory
CategoryTheory.Limits.IsZero.op
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : C},
CategoryTheory.Limits.IsZero X → CategoryTheory.Limits.IsZero (Opposite.op X)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Quiver.Homproof · cited by 32,603
- Oppositestatement and proof · cited by 8,081
- Opposite.unopproof · cited by 2,231
- Quiver.Hom.opproof · cited by 1,948
- Quiver.Hom.unopproof · cited by 903
- CategoryTheory.Limits.IsZerostatement and proof · cited by 306
- CategoryTheory.Limits.IsZero.eq_of_srcproof · cited by 57
- CategoryTheory.Limits.IsZero.eq_of_tgtproof · cited by 46
- Quiver.Hom.unop_injproof · cited by 33
- CategoryTheory.Limits.IsZero.to_proof · cited by 8
- CategoryTheory.Limits.IsZero.from_proof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.Exact.opproof · cited by 5
- HomologicalComplex.pathObject.isZero_Xproof · cited by 1
- HomologicalComplex.isStrictlySupportedOutside_op_iffproof · cited by 0
- HomologicalComplex.isStrictlySupported_op_iffproof · cited by 0
- CochainComplex.isKProjective_of_projectiveproof · cited by 0