felt like archiving a quote by Paul Taylor somewhere, it is now at *folklore*.

Besides being funny, it is actually a useful comment for the newbie, and so I linked to it from *category theory*.

collected some references on the interpretation of the !-modality as the Fock space construction at *!-modality*.

Cross-linked briefly with he stub entries_Fock space_ and *second quantization*.

gave the old entry *wedge sum* its explicit formal definition. Also added two examples.

created a minimum at *function monad* (aka “reader monad”, “environment monad”)

A student asked “What is a cobordism?” and I checked and realized that the $n$Lab entry *cobordism* was effectively empty.

So I have now added some basic text in the Idea-section and added a bare minimum of references. Much more should be done of course, but at least now there are pointers.

]]>I started comma double category. Since I care about equipments more than double categories in general, and because it actually is an instance of a comma object, I made the article mostly about virtual double categories. I wrote down a couple of conjectures about when the comma has units and composites, but haven’t verified them yet and not sure when I will.

]]>added references to *essentially algebraic theory*. Also equipped the text with a few more hyperlinks.

added a little bit more to *split exact sequence*.

a stubby minimum at *maybe monad*

(we are talking about it in the other thread, but for completeness I suppose I should start a new thread for it here)

]]>I created *separator*, while having the nagging feeling that we already have this entry. Of course after creating it I remembered the page *generator*.

So we should merge the stuff. Might this be an occasion to merge *away* from *generator*? A set of “generating objects” also means other things than “separating objects” (notably colimit generation). So I’d be inclined to move all material to *separator*. That would also allow to drop the warning at the beginning of *generator*.

I finally created an entry *internal category in homotopy type theory*.

There is old discussion of this topic which I had once written at *category object in an (infinity,1)-category* in the sub-section *HoTT formulation*, but it’s probably good to give this a stand-alone entry, for ease of linking (such as from *equivalence of categories* now).

I have turned *logos* from a redirect to *Heyting category* into a stand-alone disambiguation entry, to account for Joyal’s proposal from 2008 (maybe meanwhile abandoned?) to say “logos” for “quasi-category”.

edited dualizable object a little, added a brief paragraph on dualizable objects in symmetric monoidal $(\infty,n)$-categories

]]>created an entry *[[modal type theory]]*; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with *[[monad (in computer science)]]*.

edited [[reflective subcategory]] and expanded a bit the beginning

]]>slightly edited *AT category* to make the definition/lemma/proposition-numbering and cross-referencing to them come out.

Probably Todd should have a look over it to see if he agrees.

]]>Todd,

when you see this here and have a minute, would you mind having a look at *monoidal category* to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?

Thanks!

]]>created Cisinski model structure

]]>quickly added at [[accessible category]] parts of the MO discussion here. Since Mike participated there, I am hoping he could add more, if necessary.

]]>started a bare minimum at *state monad*

following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.

Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.

]]>I have given *Grothendieck construction for model categories* its own entry, in order to have a place for recording references. In particular I added pointer to the original references (Roig 94, Stanculescu 12)

(There used to be two places in the entry *Grothendieck construction* where an attempt was made to list the literature on the model category version, but they didn’t coincide and were both inclomplete. So I have replaced them with pointers to the new entry.)

added to the references-section of the stub *type-theoretic model category* pointers to André Joyal’s slides on “typoses” (he is currently speaking about that again at CRM in Barcelona).

(maybe that entry should be renamed to “categorical semantics for homotopy type theory” or the like, but I won’t further play with it for the time being).

I am also pointing to Mike’s article and to his course notes. I will maybe ask André later, but I am a bit confused about (was already in Halifax) how he presents his typoses, without mentioning of at least very similar categorical semantics that has been discussed before. Maybe I am missing some sociological subtleties here.

]]>I have added to the entry *split idempotent* the statement (here) that in a triangulated category in which the direct sum of two triangles is a triangle, then idempotents split.

(Maybe that should rather go into the entry *Cauchy complete category*?)

created a bare minimum at *sharp map*