A Remark on Static Animations

Abstract

We record a general condition guaranteeing that the animation of a small $1$-category remains a $1$-category. The proof is extremely elementary universal algebra. This recovers as a very special case the striking observation of Antieau, \cite{Ant}, that the animation of $\fnt^{\mathrm{op}}$ is a $1$-category. Our result is a fair amount more general, and for example applies to $\fnt^{\mathrm{op}}_{\mathcal{G}}$ with $\mathcal{G}$ a groupoid, as well as beyond this.