nLab fibration of (∞,1)-operads

Definition

In the sense of Lurie, def. 2.1.2.10:

a morphism of (∞,1)-operads such that the underlying map of (∞,1)-categories of operators is a fibration in the model structure for quasi-categories

Properties

Relation to $(\infty,1)$-Algebras over an $(\infty,1)$-operad

For $\mathcal{C}^\otimes \to \mathcal{O}^\otimes$ a fibration of $(\infty,1)$-operads, then for $\mathcal{P}^\otimes \to \mathcal{O}^\otimes$ any other homomorphism, an (∞,1)-algebra over $\mathcal{P}^\otimes$ in $\mathcal{C}^\otimes$ is a homomorphism of (∞,1)-operads from $\mathcal{P}$ to $\mathcal{C}$ over $\mathcal{O}$

(Lurie, def. 2.1.3.1)

Related concepts

• morphism of (∞,1)-operads

  • fibration of (∞,1)-operads

  • coCartesian fibration of (∞,1)-operads

• Kan fibration, anodyne morphism

• right/left Kan fibration, right/left anodyne map

• inner fibration

• Cartesian fibration

References

Def. 2.1.2.10

• Jacob Lurie, Higher Algebra