A semi-Segal space is a semi-simplicial object in such that
A semi-simplicial object being Reedy fibrant means that for each the morphisms
A complete semi-Segal space is a semi-Segal space such that the two morphisms
are weak equivalences.
A semi-Segal space is quasiunital if (…)
A morphism of complete semi-Segal spaces is quasi-unital if it preserves the weak equivalences, hence if
The notion is mentioned in
More details are spelled out in