nLab
fibration of (∞,1)-operads

Contents

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 (,1)(\infty,1)-Algebras over an (,1)(\infty,1)-operad

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

(Lurie, def. 2.1.3.1)

References

Def. 2.1.2.10

Last revised on February 11, 2013 at 16:01:16. See the history of this page for a list of all contributions to it.