Take $x$. Subtract and add $1$ and then multiply. I am still very confused by the fact that it gives $x^2-1$ and not $x^2$.

@NicolasHemelsoet Thanks for your comment! Are you able to unravel what it means in this particular situation?

@LSpice Thanks for your comment! $A^{\otimes [n]}$ indeed has $n+1$ tensor factors (and lives in degree $n$).

A curiosity: modeling $\infty$-categories by weak Kan complexes, thanks to the definition you mention, one could define homotopy groups of a $\infty$-category $\mathcal{C}$ (say, pointed by an initial object). Is there an interpretation of these, e.g. when $\mathcal{C}$ is the nerve of an ordinary category?

The reference of Grayson is helpful, thanks @DanRamras !