nLab semiadditive dagger category

Contents

Contents

Definition

A semiadditive dagger category is a cocartesian monoidal dagger category (C,,0,i A,i B,0 A)(C, \oplus, 0, i_A, i_B, 0_A) such that

  • for all objects AOb(C)A \in Ob(C), i A i A=id Ai_A^\dagger \circ i_A = id_A and i A i A=id Ai_A^\dagger \circ i_A = id_A
  • for all objects AOb(C)A \in Ob(C) and BOb(C)B \in Ob(C), i B i A=0 B0 A i_B^\dagger \circ i_A = 0_B \circ 0_A^\dagger

In a semiadditive dagger category, the coproduct is called a biproduct and the initial object is called a zero object.

Examples

See also

References

  • Martti Karvonen. Biproducts without pointedness (abs:1801.06488)
  • Chris Heunen and Martti Karvonen. Limits in dagger categories. Theory and Applications of Categories, 34(18):468–513, 2019.
  • Chris Heunen, Andre Kornell. Axioms for the category of Hilbert spaces (arXiv:2109.07418)

Created on May 3, 2022 at 22:06:10. See the history of this page for a list of all contributions to it.