Abstract:We show that the classifying space functor B : Mon → Top * from the category of topological monoids to the category of based spaces is left adjoint to the Moore loop space functor : Top * → Mon after we have localized Mon with respect to all homomorphisms whose underlying maps are homotopy equivalences and Top * with respect to all based maps which are (not necessarily based) homotopy equivalences. It is well-known that this localization of Top * exists, and we show that the localization of Mon is the category… Show more
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