Theorems · Inductive type · category theory
CategoryTheory.Limits.HasFiniteBiproducts
(C : Type uC) → [inst : CategoryTheory.Category.{uC', uC} C] → [CategoryTheory.Limits.HasZeroMorphisms C] → PropA category HasFiniteBiproducts if it has a biproduct for every finite family of objects in C
indexed by a finite type.
- Cited by
- 106 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 by132
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.biproduct.matrixstatement and proof · cited by 22
- CategoryTheory.leftDistributorstatement and proof · cited by 15
- CategoryTheory.rightDistributorstatement and proof · cited by 15
- CategoryTheory.Limits.biproduct.matrix_πstatement and proof · cited by 7
- CategoryTheory.HomOrthogonal.matrixDecompositionstatement and proof · cited by 6
- CategoryTheory.Mat_.liftstatement and proof · cited by 6
- CategoryTheory.Limits.biproduct.componentsstatement and proof · cited by 5
- CategoryTheory.HomOrthogonal.matrixDecompositionAddEquivstatement and proof · cited by 4
- CategoryTheory.Limits.kernelForkBiproductToSubtypestatement and proof · cited by 4
- CategoryTheory.Idempotents.Karoubi.Biproducts.biconestatement and proof · cited by 4
- CategoryTheory.Limits.cokernelCoforkBiproductFromSubtypestatement and proof · cited by 4
- CategoryTheory.leftDistributor_homstatement and proof · cited by 4