Example [efr-0038]

For any category \mathcal {C}, a Segal object where C[0] is terminal is equivalently a monoid object in \mathcal {C} (with the Cartesian monoidal structure). In particular, a (strict) Segal object in \mathsf {Cat} is a strict monoidal category. On the other hand, a weak Segal object is equivalently a (not necessarily strict) monoidal category.