Also have given the entry an Idea-section, now here.

]]>while I was at it, I have beautified the typesetting of the classical definition (here)

]]>added historical references:

Beware that the term “monoid” was first used by

- Arthur Cayley,
*Second and Third Memoirs on Skew Surfaces*, Otherwise Scrolls, Phil. Trans. (1863 and 1869)

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

- Garrett Birkhoff,
*Hausdorff Groupoids*, Annals of Mathematics, Second Series**35**2 (1934) 351-360 [jstor:1968437, doi:10.2307/1968437]

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.

]]>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 section about the finite product/sums in a monoid

Anonymous

]]>(note that #6 is meant to be about the HoTT topic page on “Monoid”)

]]>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.

]]>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 $\infty\! Gpd$”?

]]>Added a reference.

]]>Moved examples and other material to the page monoid in a monoidal category’

]]>Thanks!

]]>typo

dorchard

]]>I thought it worthwhile to add the view of monoids as strict monoidal categories. This seems missing here.

dorchard

]]>