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rather: smash product [ edit, ah, I see you changed it ]
Original author here: this article was created because I was making articles for oidifications of various algebraic structures (i.e. differential algebroid for differential algebra); I seemed to have forgotten to put in an ideas section when writing this article; this should be the oidification of an absorption monoid.
Anonymous
Is the terminology “absorption category” something that occurs in the literature?
(Maybe the same type of terminological question could be asked of many articles in this proliferation of oidification articles.)
There is decidedly no requirement for Lab contributions (including concepts and notation) to be confined to what already occurs in the literature. On the contrary, where this is the case it tends to serve as background material for other contributions that the author cares to record here precisely because they are not yet in the literature, or not in a given form or from a given perspective. This explicit contrast to other places, like Wikipedia or also the StacksProject (I suppose) etc. got enshrined in the pun of the nPOV.
This policy makes contributing to and reading of the Lab potentially more interesting but also potentially more risky than at other places, because it means that material that appears may not have been vetted and not have been “peer reviewed”, certainly not the moment it is becomes visible on published Lab pages.
Another crucial aspect of the Lab is that there is in practice no bounds on resources. As long as contributions are sane and of potential use to at least the author themselves, there is no harm having them.
In the present case, my understanding is that our “Guest” set themselves the goal of making explicit the oidification of a whole list of common basic notions of algebra, and, for completeness, to introduce/invent the (mostly evident) terminology where not yet established.
I think that’s clearly sane, plausibly of potential interest to various readers even if not to others (as it goes) and in fact potentially a good basis for establishing a lot of cross-links between existing and not-yet existing entries.
There is an evident question of design decision: Given that most of these oidifications are straightforward and done justice by just a few lines of text, one might have decided to keep them all in a list on a single Lab page. On the other hand, as soon as anyone actually does want to explicitly refer to any item in this list, it is much more convenient for both author and their readers if that item has its own entry. And since, as above, there is no practical constraint on the number of entries, it doesn’t seem to hurt to have lots of little entries.
In conclusion, I see no reason to discourage our “Guest” from what they are doing. What I would do is ask to keep in mind to make clear to the reader in each and every Idea-section what kind of material it is they are being confronted with: If an entry introduces new terminology, then this is fine, but should be made crystal clear to the reader right up-front. Similarly for the purpose of the entry: If there is risk that readers might be puzzled as to what point an entry has, then it should be made clear right there in the Idea-section.
In the present case this might mean that the Idea sections should generally amplify/recall (a) the concept of oidification aka horizontal categorification and (b) the fact that there are many basic notions in algebra whose horizontal categorification either has not been considered at all, or has been considered, but under an unrelated name. And the point of all these entries is make this secret systematics of horizontal categorification more broadly explicit.
Quite in line with the nPOV, even if for “horizontal ”, here.
That seems very reasonable, Urs.
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