Theorems · Theorem · category theory
CategoryTheory.Functor.map_neg
∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Preadditive C]
[inst_3 : CategoryTheory.Preadditive D] (F : CategoryTheory.Functor C D) [F.Additive] {X Y : C} {f : X ⟶ Y},
F.map (-f) = -F.map f- Cited by
- 7 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
- AddMonoidHom.map_negproof · cited by 22
- CategoryTheory.Functor.mapAddHomproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.homologySequence_exact₁proof · cited by 5
- CategoryTheory.ShiftedHom.comp_negproof · cited by 1
- CochainComplex.mappingCone.map_δproof · cited by 1
- CategoryTheory.Abelian.Ext.mk₀_negproof · cited by 1
- AlgebraicGeometry.tilde.map_negproof · cited by 0
- CochainComplex.HomComplex.Cochain.map_negproof · cited by 0