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The long-known results of Schreier on group extensions are here raised to a categorical level by giving a factor set theory for torsors under a categorical group (G, ⊗) over a small category B. We show a natural bijection between the set of equivalence classes of such torsors and [B(B), B(G, ⊗)], the set of homotopy classes of continuous maps between the… (More)

The rank of a commutative cancellative semigroup S is the cardinality of a maximal independent subset of S. Commutative cancellative semigroups of finite rank are subarchimedean and thus admit a Tamura-like representation. We characterize these semigroups in several ways and provide structure theorems in terms of a construction akin to the one devised by T.… (More)

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