Theorems · Inductive type · category theory
CategoryTheory.Limits.HasBinaryBiproducts
(C : Type uC) → [inst : CategoryTheory.Category.{uC', uC} C] → [CategoryTheory.Limits.HasZeroMorphisms C] → PropHasBinaryBiproducts C represents the existence of a bicone which is
simultaneously a limit and a colimit of the diagram pair P Q, for every P Q : C.
- Cited by
- 165 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
Cited by230
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.trianglestatement and proof · cited by 48
- CochainComplex.mappingConeCompTrianglestatement and proof · cited by 20
- CochainComplex.mappingCone.mapstatement and proof · cited by 19
- CochainComplex.mappingCone.trianglehstatement and proof · cited by 14
- CategoryTheory.Biprod.ofComponentsstatement and proof · cited by 10
- CochainComplex.mappingConeCompHomotopyEquivstatement and proof · cited by 9
- CategoryTheory.Limits.pointwiseBinaryBiconestatement and proof · cited by 9
- CochainComplex.mappingCone.triangleRotateShortComplexstatement and proof · cited by 9
- CategoryTheory.Limits.biprod.braidingstatement and proof · cited by 9
- HomotopyCategory.Pretriangulated.distinguishedTrianglesstatement and proof · cited by 8
- CategoryTheory.Functor.additive_of_preservesBinaryBiproductsstatement and proof · cited by 7
- CochainComplex.mappingCone.mapOfHomotopystatement and proof · cited by 7
Showing the 200 most cited of 230.