Theorems · Theorem · category theory
CategoryTheory.Limits.biprod.inr_desc
∀ {C : Type uC} [inst : CategoryTheory.Category.{uC', uC} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{W X Y : C} [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X Y] (f : X ⟶ W) (g : Y ⟶ W),
CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.biprod.inr (CategoryTheory.Limits.biprod.desc f g) = g- Cited by
- 18 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Limits.biprodstatement · cited by 312
- CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
- CategoryTheory.Limits.biprod.inrstatement · cited by 109
- CategoryTheory.Limits.BinaryCofan.mkproof · cited by 83
- CategoryTheory.Limits.IsColimit.facproof · cited by 82
- CategoryTheory.Limits.biprod.descstatement · cited by 54
- CategoryTheory.Limits.BinaryBiproduct.isColimitproof · cited by 8
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.biprod.inr_desc_assocproof · cited by 7
- HomologicalComplex.cylinder.ι₁_descproof · cited by 4
- CategoryTheory.Limits.biprod.desc_eqproof · cited by 2
- CategoryTheory.Functor.inr_biprodComparison'proof · cited by 1
- CategoryTheory.Limits.biprod.mapBiprod_inv_map_descproof · cited by 1
- CategoryTheory.SemiadditiveOfBinaryBiproducts.distribproof · cited by 1
- CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_rightAddproof · cited by 1
- HomologicalComplex.inr_biprodXIso_invproof · cited by 1
- CategoryTheory.IsPushout.hom_eq_add_up_to_refinementsproof · cited by 1
- CategoryTheory.Limits.biprod.inr_opIso_invproof · cited by 1
- CategoryTheory.kernelCokernelCompSequence.inr_πproof · cited by 1
- HomologicalComplex.biprod_inr_desc_fproof · cited by 1