Theorems · Theorem · category theory
CategoryTheory.Functor.isZero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
(F : CategoryTheory.Functor C D), (∀ (X : C), CategoryTheory.Limits.IsZero (F.obj X)) → CategoryTheory.Limits.IsZero F- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.NatTrans.ext'proof · cited by 340
- 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
- CategoryTheory.Limits.IsZero.to_proof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.isZero_iffproof · cited by 3
- CategoryTheory.Limits.IsZero.objproof · cited by 3
- CategoryTheory.Functor.preservesColimitsOfShape_of_isZeroproof · cited by 1
- CategoryTheory.Functor.preservesLimitsOfShape_of_isZeroproof · cited by 1
- HomologicalComplex.isZero_single_comp_evalproof · cited by 0