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expanded endomorphism operad
(it’s still a bit rough, but I am a bit rushed and have no time to polish)
I have expanded endomorphism operad a little;
added the definition in terms of monads in -spans and mentioned from
Claudio Hermida, Representable multicategories, Adv. Math. 151 (2000), no. 2, 164-225 (pdf)
the result that forming endomorphism operads is right 2-adjoint to forming categories of operators.
(I can’t quite make myself decide on nice cross-entry consistent notation for the moment. There is lots of room to polish this up.)
I made representable multicategory redirect to endomorphism operad for the time being. Probably we want to have separate entries, eventually.
I have added pointers to “representable multicategory” from monoidal category and from multicategory. But I think that’s all that I have energy for, concerning this topic, right now.
I would like to rename endomorphism operad to representable multicategory and change the text of the page appropriately. I think that using the term “endomorphism operad” for this general notion is unjustifiable — it doesn’t actually have the original notion of “endomorprhism operad of an object” as a special case, until you further generalize it by restricting to a subset of objects — and also highly confusing, because in general it has nothing to do with endomorphisms.
I think it would be reasonable to have a separate page called endomorphism operad that is about the version that’s actually talking about endomorphisms of an object, which is barely mentioned on the current page called endomorphism operad.
Any objections?
I think I always use the (traditional) term “endomorphism operad” to mean endomorphism operad of an object, so those suggestions seem reasonable to me.
Ok, I renamed the old page “endomorphism operad” to representable multicategory, and created a new page endomorphism operad.
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