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 $R$.

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.

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

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.

Last revised on August 17, 2009 at 18:05:37. See the history of this page for a list of all contributions to it.