nLab finitely complete (infinity,1)-category

Idea

Finitely complete $(\infty,1)$-categories are the analog in (∞,1)-category theory of finitely complete categories in category theory.

Definition

Definition

Let $\mathcal{C}$ be an (∞,1)-category. This is called a finitely complete $(\infty,1)$-category if $\mathcal{C}$ has finite (∞,1)-limits, i.e.

• if it has a terminal object and (∞,1)-fiber products;
• if it has a terminal object and for every object $x \in C$, the over-(∞,1)-category $C_{/x}$ has finite products.

Related concepts

• finitely complete category

• (infinity,1)-category

• finite (infinity,1)-limit

• exact (infinity,1)-category