In mathematics, R-algebroids are constructed starting from groupoids.
These are more abstract concepts than the Lie algebroids that play a similar role in the theory of Lie groupoids to that of Lie algebras in the theory of Lie groups.
is the free R-module on the set
can be regarded as a category with invertible morphisms.
Then an R-category is defined as an extension of the R-algebroid concept by replacing the groupoid
in this construction with a general category C that does not have all morphisms invertible.
with finite support, and with the convolution product defined as follows:
[2] Only this second construction is natural for the topological case, when one needs to replace 'function' by 'continuous function with compact support', and in this case
This article incorporates material from Algebroid Structures and Algebroid Extended Symmetries on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.