In the Higher Topos Theory, Example 1.2.14.2 says “finitely presentable $\infty$-groupoids correspond precisely to the finite cell complexes” But, for example, $K(\mathbb{Z}, 2)$ is seems finitely presentable ($1$ object $*$, $0$ generating $1$-morphisms and $1$ generating $2$-morphism on $\mathrm{id}_*$) and it is not homotopy equivalent to a finite complex. Is this a mistake in the book?

UPD. Judging by this entry, my presentation is still described by $S^2$, and not by $K(\mathbb{Z}, 2)$. Then my question is: where can I read the formal definition of the presentation of $\infty$-categories by generators and relations (and in particular, understand in these terms where higher morphisms arise from here). I don't see any details from Luri yet.

In the Higher Topos Theory, Example 1.2.14.2 says “finitely presentable $\infty$-groupoids correspond precisely to the finite cell complexes” But, for example, $K(\mathbb{Z}, 2)$ is seems finitely presentable ($1$ object $*$, $0$ generating $1$-morphisms and $1$ generating $2$-morphism on $\mathrm{id}_*$) and it is not homotopy equivalent to a finite complex. Is this a mistake in the book?

UPD. Judging by this entry, my presentation is still described by $S^2$, and not by $K(\mathbb{Z}, 2)$. Then my question is: where can I read the formal definition of the presentation of $\infty$-categories by generators and relations (and in particular, understand in these terms where higher morphisms arise from here). I don't see any details from Lurie yet.

In the Higher Topos Theory, Example 1.2.14.2 says “finitely presentable $\infty$-groupoids correspond precisely to the finite cell complexes” But, for example, $K(\mathbb{Z}, 2)$ is seems finitely presentable ($1$ object $*$, $0$ generating $1$-morphisms and $1$ generating $2$-morphism on $\mathrm{id}_*$) and it is not homotopy equivalent to a finite complex. Is this a mistake in the book?

In the Higher Topos Theory, Example 1.2.14.2 says “finitely presentable $\infty$-groupoids correspond precisely to the finite cell complexes” But, for example, $K(\mathbb{Z}, 2)$ is seems finitely presentable ($1$ object $*$, $0$ generating $1$-morphisms and $1$ generating $2$-morphism on $\mathrm{id}_*$) and it is not homotopy equivalent to a finite complex. Is this a mistake in the book?

UPD. Judging by this entry, my presentation is still described by $S^2$, and not by $K(\mathbb{Z}, 2)$. Then my question is: where can I read the formal definition of the presentation of $\infty$-categories by generators and relations (and in particular, understand in these terms where higher morphisms arise from here). I don't see any details from Luri yet.