nLab
algebra in an (infinity,1)-category

Context

Higher algebra

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

Contents

Idea

Recall that a monoid object or algebra object in a monoidal category CC is the same as a lax monoidal functor

*C. * \to C \,.

This definition generalized to monoidal (∞,1)-categories and defines algebra objects for these.

Definition

For CC a monoidal (∞,1)-category with monoidal structure determined by the (∞,1)-functor

p :C N(Δ) op p_\otimes : C^\otimes \to N(\Delta)^{op}

a monoid object of CC is a lax monoidal (∞,1)-functor?

N(Δ) opC N(\Delta)^{op} \to C^\otimes

Examples

References

definition 1.1.14 in

An equivalent reformulation of commutative monoids in terms (∞,1)-algebraic theories is in

Revised on January 13, 2014 16:08:20 by Urs Schreiber (89.204.155.62)