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Homotopy Type Theory
semiadditive dagger category > history (Rev #4, changes)

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~~# Contents

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~~## Definition

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~~A **semiadditive dagger category** is a cocartesian monoidal dagger category $(C, \oplus, 0, i_A, i_B, 0_A)$ with

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- an identity $m_A: i_A^\dagger \circ i_A = id_A$ for $A:C$
- an identity $m_B: i_B^\dagger \circ i_B = id_B$ for $B:C$
- an identity $p: i_b^\dagger \circ i_A = 0_B \circ 0_A^\dagger$ for $A:C$ and $B:C$.

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

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~~## Examples

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~~(…)

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~~## See also

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~~## References

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- 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)

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