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

Idea

Recall the pattern in ordinary algebra:

Accordingly in higher algebra:

Definition

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

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

a commutative algebra object in CC is a section

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

such that AA carries collapsing morphisms in FinSet *FinSet_* to coCartesian morphisms in C C^\otimes.

Examles

References

the above definition is definition 1.19 in

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