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Thanks!
Moved examples and other material to the page monoid in a monoidal category’
A question on language; isn’t it confusing in a natively homotopy-theoretic context to give unadorned terms like “monoid” a default interpretation that is effectively “… object in Set” rather than “… object in $\infty\! Gpd$”?
I suppose one might argue that the implicit infinity-category convention should extend to writing “monoid” for $A_\infty$-space, but I haven’t heard anyone suggest it before.
(note that #6 is meant to be about the HoTT topic page on “Monoid”)
added pointer to:
Martín Escardó, The Types of Magmas and Monoids, §4 in: Introduction to Univalent Foundations of Mathematics with Agda [arXiv:1911.00580, webpage]
added historical references:
Beware that the term “monoid” was first used by
for certain surfaces, quite unrelated to the modern meaning of the term.
Instead, what are now called monoids (unital associative magmas) were called groupoids (now clashing with the modern use of groupoid) by
The modern terminology “monoid” for unital associative magmas is (according to Hollings 2009, p. 529) due to
For more on the history of the notion:
Christopher Hollings, The Early Development of the Algebraic Theory of Semigroups, Archive for History of Exact Sciences 63 (2009) 497–536 [doi:10.1007/s00407-009-0044-3]
Math.SE, Who invented Monoid?
It would be good to add more precise pointer to where Bourbaki introduces the terminology.
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