nLab (infinity,1)-pushout

Idea

An $(\infty,1)$-pushout is a colimit in an (∞,1)-category $\mathcal{C}$ over a diagram of the shape

$$\{a \leftarrow c \to b\} \to \mathcal{C} \,.$$

In other words it is a cocone

$$\array{ C &\to& B \\ \downarrow &\cong\swArrow& \downarrow \\ A &\to& A \sqcup_C B }$$

which is universal among all such cocones in the $(\infty,1)$-categorical sense.

This is the analog in (∞,1)-category theory of the notion of pushout in category theory.

Related concepts

• (infinity,1)-pullback
• (infinity,1)-coproduct
• (infinity,1)-colimit