Comparison of the Plus and Q-Constructions
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Let S be an abelian monoid i.e. S has a commutative, associative binary operation with a 2-sided identity. We say that S acts on a set X if there is a homomorphism of monoids S → Hom Set (X, X); if s ε S, the corresponding map of sets X → X is called translation by s. We say that S acts invertibly on X if each translation is bijective.
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