An absorption category or annihilation category$C$ is a category where for every two objects $a, b \in Ob(C)$ there is a morphism $0_{a\to b}: a \to b$, such that for any objects $a, b, c, d \in Ob(C)$, for any morphism $f:b \to c$, $f \circ 0_{a\to b} = 0_{a\to c}$, and for any morphism $g:d \to a$, $0_{a\to b} \circ g = 0_{d\to b}$.