# Idea

Recall the pattern in ordinary algebra:

Accordingly in higher algebra:

# Definition

A commutative algebra object in a symmetric monoidal (infinity,1)-category $C$ is a lax symmetric monoidal $(\infty,1)$-functor

$* \to C \,.$

In more detail, this means the following:

###### Definition

Given a symmetric monoidal (infinity,1)-category in its quasi-categorical incarnation as a coCartesian fibration of simplicial sets

$p : C^\otimes \to N(FinSet_*)$

a commutative algebra object in $C$ is a section

$A : N(FinSet_*) \to C^\otimes$

such that $A$ carries collapsing morphisms in $FinSet_*$ to coCartesian morphisms in $C^\otimes$.

# References

the above definition is definition 1.19 in

Revised on September 15, 2009 15:39:41 by Urs Schreiber (195.37.209.182)