Theorems · Theorem · category theory
CategoryTheory.Preadditive.comp_sub
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C] {P Q R : C} (f : P ⟶ Q)
(g g' : Q ⟶ R),
CategoryTheory.CategoryStruct.comp f (g - g') =
CategoryTheory.CategoryStruct.comp f g - CategoryTheory.CategoryStruct.comp f g'- Defined in
- Mathlib.CategoryTheory.Preadditive.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
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_subproof · cited by 565
- CategoryTheory.Preadditive.leftCompproof · cited by 6
Cited by23
Results whose statement or proof uses this declaration.
- CategoryTheory.Triangulated.TStructure.from_truncGE_obj_extproof · cited by 4
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_mono'proof · cited by 3
- AlgebraicTopology.DoldKan.Q_f_naturalityproof · cited by 2
- AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_fproof · cited by 2
- CategoryTheory.Idempotents.idem_of_id_sub_idemproof · cited by 2
- CochainComplex.Lifting.comp_coe_cocyle₁'_v_eq_zeroproof · cited by 2
- CategoryTheory.Preadditive.isSeparator_iffproof · cited by 2
- CategoryTheory.Abelian.SpectralObject.cokernelSequenceE_exactproof · cited by 2
- CochainComplex.isKInjective_of_injective_auxproof · cited by 1
- CategoryTheory.ObjectProperty.isLocal_trWproof · cited by 1
- CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_invproof · cited by 1