Theorems · Definition · category theory
CochainComplex.mappingCocone.fst
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{K L : CochainComplex C ℤ} →
(φ : K ⟶ L) → [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] → CochainComplex.mappingCocone φ ⟶ KThe first projection mappingCocone φ ⟶ K.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Preadditivestatement and proof · cited by 3,309
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
- CochainComplex.mappingCone.fstproof · cited by 51
- CochainComplex.mappingCoconestatement · cited by 46
- CochainComplex.HomComplex.Cocycle.homOfproof · cited by 9
- CochainComplex.HomComplex.Cocycle.leftShiftproof · cited by 8
Cited by15
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCocone.triangleproof · cited by 6
- CochainComplex.mappingCocone.liftCochain_v_fst_fstatement · cited by 3
- CochainComplex.mappingCocone.lift_f_fst_fstatement and proof · cited by 2
- CochainComplex.mappingCocone.inl_v_fst_fstatement · cited by 1
- CochainComplex.mappingCocone.inr_v_fst_fstatement · cited by 1
- CochainComplex.mappingCocone.lift_fststatement and proof · cited by 1
- CochainComplex.mappingCocone.id_Xstatement · cited by 0
- CochainComplex.mappingCocone.inl_v_fst_f_assocstatement and proof · cited by 0
- CochainComplex.mappingCocone.inr_v_fst_f_assocstatement and proof · cited by 0
- CochainComplex.mappingCocone.liftCochain_comp_fststatement and proof · cited by 0
- CochainComplex.mappingCocone.liftCochain_v_fst_f_assocstatement and proof · cited by 0
- CochainComplex.mappingCocone.lift_f_fst_f_assocstatement and proof · cited by 0