  We follow the work of Aguiar on internal categories and introduce simplicial
objects internal to a monoidal category as certain colax monoidal functors.
Then we compare three approaches to equipping them with a discrete set of
vertices. We introduce based colax monoidal functors and show that under
suitable conditions they are equivalent to the templicial objects defined in
arXiv:2302.02484v2. We also compare templicial objects to the enriched Segal
precategories appearing in the work of Lurie, Simpson and Bacard, and show that
they are equivalent for cartesian monoidal categories, but not in general.
