The tight groupoid of the inverse semigroups of left cancellative small categories
Peer reviewed, Journal article
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We fix a path model for the space of filters of the inverse semigroup associated to a left cancellative small category . Then, we compute its tight groupoid, thus giving a representation of its -algebra as a (full) groupoid algebra. Using it, we characterize simplicty for these algebras. Also, we determine amenability of the tight groupoid under mild, reasonable hypotheses.