0
votes
1answer
32 views

Can the integral group ring construction be extended to groupoids in such a way that it provides a functor from Groupoids to Rings?

If $G$ is a group, and $R$ is a ring, one can construct the group ring $R[G]$, which is a free $R$-module with basis $G$, and with multiplication coming from the original multiplication of $G$. ...
0
votes
1answer
39 views

Proving closure of unit space of a Hausdorff groupoid

For Hausdorff topological groups, the set $\{e\}$ containing only the identity is closed. This is because Hausdorff implies T1 which implies singletons are closed. For topological groupoids, defined ...
3
votes
2answers
69 views

Is a groupoid a universal algebra?

I was trying to use the first isomorphism theorem on groupoids. From the wikipedia page I know that it holds for groups, rings and algebras. So are groupoids algebras? Or, in other words, does the ...
6
votes
4answers
912 views

definition of a groupoid

Notation: Underlining $\underline{G}$ denotes a category and $\underline{G}(x,y)$ the class of morphisms from $x$ to $y$. On the Wiki page about groupoids, it is written (I write here my own more ...