Okay, thanks. I have added a brief pointer to your HoTT posting to the entry.

]]>I suppose that would be good. Maybe there should be an nLab entry. But I don’t really have time to write out any details right now…

]]>Mike,

what would be the preferred way to cite your result that generalizes the equivalence “stable” = “comes from lex reflector” for reflective factorization systems as stated at *stable factorization system - stable reflective factorization systems*, but now generalized from categories to $\infty$-categories?

Your blog notes? Our QFT writeup? Should we have an $n$Lab entry on it?

In either case, I’d like to have a stable (though not necessarily reflective) way to cite this.

]]>Yes, once you know also that dependent sums preserve n-truncated types.

]]>still says

Ah, sorry. Fixed now. (I should stop editing entries in a haste at a bus stop…)

I think stability of the n-connected/n-truncated factorization system is HTT 6.5.1.16(6).

Ah, great. I had missed that. Thanks!!

But still my question: in the type theory $n$-truncation is a reflection on $Type$. Does that not also directy imply the statement?

]]>The examples section at stable factorization system still says “In an a topos, epimorphism are stable under pullback and hence the (epi, mono) factorization system in an adhesive category is stable”.

I think stability of the $n$-connected/$n$-truncated factorization system is HTT 6.5.1.16(6).

]]>I had fixed it by #3.

Here is a question: how known is it that the $n$-connected/$n$-truncated factorization system in an $\infty$-topos is stable?

(For $n = -1$ this is in HTT, of course. I suppose generally it follows directly from the fact that truncation is an idempotent monad on $Type$? )

]]>I missed something — why does an adhesive category even have (epi,mono) factorizations?

]]>So I fixed something here and there.

Eventually I really wanted to put more examples there. But not right now.

]]>ah, do I need to say “co-adhesive”? I should fix that, but my bus is about to arrive…

]]>added in an Examples-section to *stable factorization system* the statement that in an adhesive category, in particular in a topos, the (epi, mono)-factorization is stable.