Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
this article uses query boxes, which is against the recommendation of the “Anything I shouldn’t do?” section of the writing in the nLab article. Should the query boxes be removed?
based upon the advice given here I’m going ahead and removing the query boxes from the articles:
+–{: .query} David Roberts: How do Lie algebroids fit into this framework?
Urs Schreiber: at a rough level it is clear that the base space of a Lie algebroid has to be regardedas the “space of objects”. Certainly a Lie algebroid over a point is precisely a Lie algebra.
But for a more precise statement one needs a more conceptual way to think of Lie algebroids. I am claiming at ∞-Lie algebroid (schreiber) that there is a way to regard Lie algebroids precisely as certain kinds of synthetically smooth groupoids, namely those all whose morphisms have “infinitesimal extension” in some sense. In such a picture Lie algebroids are on the same footing as Lie groupoids and are precisely the many-object version of Lie algebras = infinitesimal Lie groups.
=–
+–{: .query} Mike: Is there (and do we want there to be) a general rule about whether an X-oid means an internal category whose one-object version is an X, or an enriched category whose one-object version is an X? The examples above seem to be taking the “internal” side, but the Cafe discussion on “ringoids” was about the “enriched” version; the two are very different! And “dg-algebroid” was suggested for dg-category, which is an enriched oidification of a dg-algebra, but a Hopf algebroid is an internal oidification of a Hopf algebra.
Urs: good point. We should say this at the beginning and split the list of examples in two sorts =–
Anonymous
Does horizontal categorification yield strict categories or univalent categories?
Applied the pedantic fix which I always apply in this situation (not picking at you, specifically, but hoping my appeal will be heard eventually):
Namely, speaking of
categorification of a monad
does not type-check, does it.
I have changed it to
the categorification of the notion of monads
I’d be fine with abbreviating this to
the categorification of monads
as ordinary people do; but among category/type-theorists we might as well say it properly. :-)
1 to 8 of 8