ScalingStacks

Definition 2.3. A set can be regarded as a $1$-category with only identity morphisms, and this defines a fully faithful functor

$$\cat_{0}\hookrightarrow\cat_{1}$$

that respects products. Passing to enriched categories then yields a sequence of fully faithful functors

$$\cat_{0}\hookrightarrow\cat_{1}\hookrightarrow\cdots\hookrightarrow\cat_{(n-1)}\hookrightarrow\cat_{n}\hookrightarrow\cdots.$$

We will tacitly treat these functor as inclusions in order to treat strict $k$-categories as examples of strict $n$-categories when $0\leq k\leq n$. In particular, a strict $n$-categories in the image of $\cat_{0}$ under this inclusions will be called discrete.