20,630 research outputs found
Completely inverse -groupoids
A completely inverse -groupoid is a groupoid satisfying the
identities , and , where
is a unique inverse of , that is, and
. First we study some fundamental properties of such
groupoids. Then we determine certain fundamental congruences on a completely
inverse -groupoid; namely: the maximum idempotent-separating
congruence, the least -group congruence and the least -unitary
congruence. Finally, we investigate the complete lattice of congruences of a
completely inverse -groupoids. In particular, we describe congruences
on completely inverse -groupoids by their kernel and trace
Limits over categories of extensions
We consider limits over categories of extensions and show how certain
well-known functors on the category of groups turn out as such limits. We also
discuss higher (or derived) limits over categories of extensions.Comment: 18 page
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