defn - fractal infinity category

Definition A pointed $\infty$-category $C$ admitting finite products is said to be fractal if the functor

$Aut:C\to Gp(C)$ is an equivalence.

Remark

• This says 0-groups coincide with 1-groups, hence the fully invertible part of the categorification tower is constant.

Examples

• the 0-category (0-object in pointed categories) is fractal
• $\infty$-categories of formal moduli problems are fractal.

Construction of Aut

Mimicking the construction in constr - unpointed toposic Koszul duality. This was also constructed in the work of Hoyois-Safranov-Schrotzeke-Sibilla on categorified traces.