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Residually linear abstract groupoids
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We introduce the notion of residually linear groupoids. We characterize this class in analogy with the group-theoretic setting.
Various properties are proved and a relationship with residual finiteness is investigated.
From a categorical point of view, our approach extends some well-known results in the theory of discrete groups, due mainly to Mal'cev and Menal. Finally, as an application, we show that the character groupoid of the Hopf algebroid of representative functions of a transitive groupoid is always residually linear.
Steklov Mathematical Institute
Title: Residually linear abstract groupoids
Description:
We introduce the notion of residually linear groupoids.
We characterize this class in analogy with the group-theoretic setting.
Various properties are proved and a relationship with residual finiteness is investigated.
From a categorical point of view, our approach extends some well-known results in the theory of discrete groups, due mainly to Mal'cev and Menal.
Finally, as an application, we show that the character groupoid of the Hopf algebroid of representative functions of a transitive groupoid is always residually linear.
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