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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

My reference for this is now Corollary 11.7 in J. P. May. The geometry of iterated loop spaces. Springer-Verlag, Berlin, 1972. Lectures Notes in Mathematics, Vol. 271.
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