Theorems · Theorem · category theory
CategoryTheory.Localization.liftNatTrans_zero
∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
(L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C) [inst_3 : L.IsLocalization W]
(F₁ F₂ : CategoryTheory.Functor C E) (F₁' F₂' : CategoryTheory.Functor D E)
[inst_4 : CategoryTheory.Localization.Lifting L W F₁ F₁'] [inst_5 : CategoryTheory.Localization.Lifting L W F₂ F₂']
[inst_6 : CategoryTheory.Limits.HasZeroMorphisms E], CategoryTheory.Localization.liftNatTrans L W F₁ F₂ F₁' F₂' 0 = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
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.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- CategoryTheory.Limits.zero_compproof · cited by 339
- CategoryTheory.Localization.Liftingstatement and proof · cited by 41
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