4 papers
Categorified groupoid-sets and their Burnside ring
Laiachi El Kaoutit, Leonardo Spinosa
We explore the category of internal categories in the usual category of (right) group-sets, whose objects are referred to as categorified group-sets. More precisely, we develop a n…
On Burnside Theory for groupoids
Laiachi El Kaoutit, Leonardo Spinosa
We explore the concept of conjugation between subgroupoids, providing several characterizations of the conjugacy relation (Theorem A in §1.2). We show that two finite groupoid-sets…
Mackey formula for bisets over groupoids
Laiachi El Kaoutit, Leonardo Spinosa
In this paper we establish the Mackey formula for groupoids, extending the well known formula in abstract groups context. This formula involves the notion of groupoid-biset, its or…
of semiartinian von Neumann regular rings. Direct finiteness versus unit-regularity
Giuseppe Baccella, Leonardo Spinosa
If is a regular and semiartinian ring, it is proved that the following conditions are equivalent: (1) is unit-regular, (2) every factor ring of is directly finite, (3)…