Theorems · Theorem · category theory
CategoryTheory.Preadditive.neg_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {P Q R : C} (f : P ⟶ Q)
(g : Q ⟶ R), CategoryTheory.CategoryStruct.comp (-f) g = -CategoryTheory.CategoryStruct.comp f g- Defined in
- Mathlib.CategoryTheory.Preadditive.Basic
- Cited by
- 31 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.
Cites6
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- map_negproof · cited by 378
- CategoryTheory.Preadditive.rightCompproof · cited by 6
Cited by31
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.homologySequence_exact₁proof · cited by 5
- HomologicalComplex.homotopyCofiber.d_sndXproof · cited by 5
- CochainComplex.HomComplex.δ_compproof · cited by 5
- HomologicalComplex.homotopyCofiber.d_fstXproof · cited by 4
- CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₁proof · cited by 3
- HomologicalComplex.homotopyCofiber.inlX_dproof · cited by 3
- CochainComplex.HomComplex.Cochain.neg_compproof · cited by 2
- CochainComplex.mappingConeCompHomotopyEquiv_comm₂proof · cited by 2
- CategoryTheory.Localization.Preadditive.neg'_eqproof · cited by 1
- CategoryTheory.Preadditive.neg_comp_negproof · cited by 1
- CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃proof · cited by 1
- CategoryTheory.ShiftedHom.comp_negproof · cited by 1