ScalingStacks

Remark 4.4. In this language, an alternative, noninductive definition of strict $n$-category is possible: a strict $n$-category $X$ is an $n$-globular set together with a family of operations $n\geq k\geq j$:

$$\ast_{j}:X_{k}\times_{X_{j-1}}X_{k}\to X_{k},$$

which are associative, unital, and suitably compatible.