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Topological semigroups/monoids: topological space endowed with a continuous semigroup/monoid structure, or, equivalently, semigroup/monoid endowed with a compatible topology.

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topological monoid from symmetric monoidal category

Well, if you are going to reference me somewhere, I can give you something more explicit. The cited Corollary 11.7 is only about topological monoids. However Theorem 4.10 of "$E_{\infty}$ spaces, g …
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