Empty Category
From ProofWiki
Theorem
Let $\mathcal C$ consist of zero objects and zero morphisms.
What is meant by "zero" here? The term "zero" on this site means a lot of more or less specialized things, one of which are an attempt to codify in abstract algebraic terms the concept of "zero" in the context of a mathematical structure which is subsequently shown to be isomorphic with a more-or-less "preconceived" notion of a set of "natural numbers". So it's not as easy as "just" linking to one of these. If (as I suspect) in the context of this page "zero" just means "none", then perhaps we need to put $0$. If we are concerned about referring to a concept that may not actually exist yet, we can perhaps put this into the context of an "empty set of objects" and "empty set of morphisms". But I'm not even sure that the term "set" has even been defined at the stage of making these initial category definitions.
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Then $\mathcal C$ is a category.
Proof
The statement holds vacuously.
$\blacksquare$
