The terminal category is a discrete category that, as a set, may be called the singleton. As a subset of the singleton, it is in fact a truth value, true (). In general, all of these (and their analogues in higher category theory and homotopy theory) may be called the point.
So far we have interpreted “terminal” as referring to the 1-category . If instead we interpret “terminal” in the 2-categorical sense, then any category equivalent to the one-object-one-morphism category described above is also terminal. A category is terminal in this sense precisely when it is inhabited and indiscrete. For such a category , the functor category is equivalent, but not isomorphic, to .