Strongly Homotopy-Commutative Monoids Revisited

We prove that the delooping, i. e., the classifying space, of a grouplike monoid is an $H$-space if and only if its multiplication is a homotopy homomorphism, extending and clarifying a result of Sugawara. Furthermore it is shown that the Moore loop space functor and the construction of the classifying space induce an adjunction of the according homotopy categories.

2000 Mathematics Subject Classification: Primary 55P45, 55P35; Secondary 55R35

Keywords and Phrases: H-spaces, Classifying space, Monoid, Strongly homotopy commutative, Homotopy homomorphism

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