# nLab algebra in an (infinity,1)-category

### Context

#### Higher algebra

higher algebra

universal algebra

## Theorems

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

(∞,1)-category theory

# Contents

## Idea

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

$* \to C \,.$

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

## Definition

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

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

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

$N(\Delta)^{op} \to C^\otimes$

## References

definition 1.1.14 in

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

• James Cranch, Algebraic Theories and $(\infty,1)$-Categories (arXiv)

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