nLab
quasi-pointed category

Recall that a category is a called a pointed category if it has a zero object, i.e. if it has an initial object and a terminal object and both are isomorphic.

For a quasi-pointed category the last condition is relaxed.

Definition

A category is quasi-pointed if it has an initial object $0$, a final object $1$ and its unique arrow $0\to 1$ is a monomorphism.

References

• D. Bourn, $3\times 3$ lemma and protomodularity, J. algebra 236 (2001), 778–795