To flesh out the sibling comment with formality: the periodic table of categories [0] gives the zero-dimensional objects as "trivial". This isn't to say that th

To flesh out the sibling comment with formality: the periodic table of categories [0] gives the zero-dimensional objects as "trivial". This isn't to say that they're empty, or just points, even though those are both reasonable interpretations. It means that there's not really anything predictable or deducible. The number of deductions is zero, but also, the dimension of the largest possible proof is zero, the dimension of the largest possible diagram is zero, etc. There's not just nothing there, but nothing constructible. Nonetheless the trivial objects exist, which is enough to allow us to draw arrows to/from them, and those arrows are not zero-dimensional. So these trivial objects show up as trivial endpoints in situations where there's only one of something. [0] https://ncatlab.org/nlab/show/periodic+table https://ncatlab.org/nlab/show/periodic+table