nLab
commutative monoid in a symmetric monoidal (infinity,1)-category

Context

(,1)(\infty,1)-Category theory

Monoidal categories

Higher algebra

Contents

Definition

(…) symmetric monoidal (∞,1)-category (…)

(,1)(\infty,1)-Category of commutative monoids

Definition

For CC a symmetric monoidal (∞,1)-category write CMon(C)CMon(C) for the (,1)(\infty,1)-category of commutative monoids in CC.

Properties

Theorem

This is (Lurie, section 4).

Corollary

(,1)(\infty,1)-Colimits over simplicial diagrams exists in CMon(C)CMon(C) and are computed in CC if they exist in CC and a preserved by tensor products.

Because the simplex category is a sifted (infinity,1)-category (as discussed there).

Examples

References

Revised on August 12, 2014 18:12:28 by Urs Schreiber (24.213.171.170)