# Idea

A locally modeled monoid or, $R$-Ring, is a generalized quantity in the sense of space and quantity which is modeled on a category of local models $R$.

# Definition

Let $(R,U,L,A)$ be a category of local models. Then an $R$-ring or monoid locally modeled on $R$ is a co-presheaf

$R \to Set$

which preserves the limits of shape in $L$.

A morphism of such locally modeled monoids is a natural transformation.

# Examples

• for $R = Ring^{op}$, $R$-rings are just ordinary rings.
• for $R =$ CartSp, $R$-rings are generalized smooth algebras.

# References

This is definition 1.1.6 of

• David Spivak, Quasi-smooth derived manifolds, PhD thesis, Berkeley (2007) (pdf)

where it appears as part of the discussion of derived smooth manifolds.

Revised on August 17, 2009 18:05:37 by Toby Bartels (71.104.230.172)