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On the category of finitely generated free groups (1609.06599v1)
Published 21 Sep 2016 in math.CT and math.GT
Abstract: It is well known that the opposite F{op} of the category F of finitely generated free groups is a Lawvere theory for groups, and also that F is a free symmetric monoidal category on a commutative Hopf monoid, or, in other words, a PROP for commutative Hopf algebras. In this paper, we give a direct, combinatorial proof of the latter fact, without using Lawvere theories.
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