ScalingStacks

Notation 6.4. The inclusion $\Upsilon_{n}\hookrightarrow\gaunt_{n}$ induces a fully faithful nerve functor

$$\nu:\gaunt_{n}\hookrightarrow\Fun(\Upsilon_{n}^{\mathrm{op}},\set).$$

In particular, we may regard gaunt $n$-categories as particular presheaves of sets on the category $\Upsilon_{n}$ (precisely which presheaves will be determined in Corollary 10.2). Note that the nerve functor commutes with all limits, hence in particular fiber products.