# Idea

Generalized smooth $L_\infty$-algebroids, or $C^\infty$-$L_\infty$-algebroids, are supposed to be the correct Lie theory-dual of infinity groupoids internal to generalized smooth spaces, $Spaces := Sheaves(CartesianSpaces)$.

Following the general lore of Space and Quantity and hence using the notion of generalized smooth algebras, a generalized smooth $L_\infty$-algebroid should be just like an L-infinity algebroid but with its defining Chevalley-Eilenberg algebra realized internal to $Quantities := CoPrSh(CartesianSpaces)$:

the algebra of functions is taken to be a C-infinity-algebra and the complex of modules is taken to be a complex of C-infinity modules.

Revised on May 29, 2012 22:04:00 by Andrew Stacey (129.241.15.200)