« first day (1876 days earlier)      last day (1527 days later) » 

Saal Hardali
Saal Hardali
5:14 AM
@TylerLawson Cool example, thanks!
 
 
4 hours later…
Andrea Gagna
Andrea Gagna
9:19 AM
@MarkPenney It is a pushout in the category of dendroidally posets (and also in the category of operads, I guess), but not in the category of dendroidal sets, in general: roughly, the pushout of the dendroidal nerve of the span defining the grafting is a dendroidal set which has the compositions of the tree above, the compositions of the tree below but not the mixed ones.
As a simple example, think about the the difference between the nerve of the simplex [2] (as a grafting of two copies of [1] in Pos or in Cat) and the pushout of the nerve of that span in simplicial sets, which is the spine of [2].
 
 
3 hours later…
Saal Hardali
Saal Hardali
12:17 PM
Another basic question about localization:
Let $C$ be a presentable monoidal $\infty$-category and let $\mathcal{L} \hoorightarrow C$ be a reflective localization of $C$. Suppose that the equivalences in $\mathcal{L}$ are stable under tensor product with objects of $C$ so that we can induce the monoidal structure on $\mathcal{L}$. Must this be homology localization then? i.e. a localization w.r.t. all morphisms which become equivalences after tensoring with some fixed collection of objects of $C$
 
 
3 hours later…
Rune Haugseng
Rune Haugseng
3:14 PM
@MarkPenney Grafting of trees is a colimit in the dendroidal category, and also in the subcategory with only inert maps (= embeddings of subtrees). (One place I believe this is discussed is in Joachim Kock's paper on polynomial functors and trees.)
 
 
3 hours later…
Charles Rezk
Charles Rezk
6:28 PM
@SaalHardali How about $C=$ infinity groupoids, $\mathcal{L}=$ sets, $\otimes=\times$?
 
 
1 hour later…
Charles Rezk
Charles Rezk
7:38 PM
I need a computer algebra package for doing calculations in a plethory.
 
Saal Hardali
Saal Hardali
@CharlesRezk Of course, silly of me to miss that. Thanks!
A homology localization is always monoidal in the sense i described though right? Do you know if there's any neat implication in the other direction (monoidal $\implies$ homology) under some suitable assumptions perhaps?
Another totally unrelated question for the general audience:
Is there a model structure on the category of presheaves on compact hausdorff spaces which presents the $\infty$ category of $\infty$ groupoids?
 
Charles Rezk
Charles Rezk
7:57 PM
@SaalHardali If I think about this, the first thing I worry about is the fact the category of compact Hausdorff spaces isn't small. (This doesn't imply such a model structure is impossible, it just makes me worry.)
 
Saal Hardali
Saal Hardali
8:10 PM
That's a good point. I didn't really think about this a lot, just interested whether anyone has.
 

« first day (1876 days earlier)      last day (1527 days later) »