Contents

category theory

# Contents

## Definition

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

• for all objects $A \in Ob(C)$, $i_A^\dagger \circ i_A = id_A$ and $i_A^\dagger \circ i_A = id_A$
• for all objects $A \in Ob(C)$ and $B \in Ob(C)$, $i_B^\dagger \circ i_A = 0_B \circ 0_A^\dagger$

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