901 reputation
11122
bio website preschema.com
location Essen, Germany
age 23
visits member for 4 years, 9 months
seen yesterday

Sep
16
comment Can the Grothendieck ring of varities over a field $k$ be defined for non separated schemes?
@Ari, the question is not about the Grothendieck group $K_0(X)$ of a scheme X, but about the Grothendieck ring $K_0(Sch_k)$ of all (separated, finite type) k-schemes.
Sep
15
comment Are these two “FUNCTORS” adjoint?
I guess this is what the OP has in mind: ncatlab.org/nlab/show/spectrum+of+an+abelian+category
Sep
13
comment What is a stable $(n,1)$-category?
For n=2 there are apparently several definitions in the literature, see the overview article arxiv.org/abs/0904.0078.
Sep
7
comment Algebraic K-theory and Homotopy Sheaves
@user125763, I added a reference which seems to discuss this (though I haven't had a chance to look at it myself yet).
Sep
7
revised Algebraic K-theory and Homotopy Sheaves
added a reference
Sep
7
revised Algebraic K-theory and Homotopy Sheaves
some clarification about the proof
Sep
7
awarded  Necromancer
Sep
6
answered Algebraic K-theory and Homotopy Sheaves
Sep
5
revised A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category
Corrected attribution of model structure on dg-categories
Sep
5
comment A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category
@MauroPorta, Lurie's construction does work in great generality, but probably is not that useful for practical purposes because one cannot really get a handle on this "chunk" (I am referring to Lemma A.3.4.6). For this reason I think the question raised by Francesco of in which generality the construction of Toën using quasi-functors works, is interesting.
Sep
5
suggested suggested edit on A general theory of quasi-functors, generalizing from dg-categories to $\mathcal V$-categories, with $\mathcal V$ monoidal model category
Aug
28
awarded  Fanatic
Aug
25
comment what is the stabilization of pointed sets?
@tetrapharmakon, in general, if $C$ is a cocomplete and complete 1-category then its nerve $N(C)$ is the infinity-category generated by the trivial model structure on $C$.
Aug
14
comment Are the pullback functors of adjoint functors also adjoint?
If I recall correctly you can find this statement in SGA 4, in the exposé about functoriality of presheaf categories.
Aug
13
comment When do limits and colimits of infinity-categories commute?
Under appropriate assumptions one has: Proposition 5.3.3.3: filtered colimits commute with finite limits. And Lemma 5.5.8.11: sifted colimits commute with finite products.
Aug
7
comment (Homotopy) limits and colimits in a dg-category
This discussion on Kan extensions in simplicially enriched categories should translate directly to the dg-setting: ncatlab.org/nlab/show/homotopy+Kan+extension#InKanCplCat One then gets (co)limits as a special case. Alternatively, "most" dg-categories are actually dg-enriched model categories, and one can use the notion of homotopy (co)limit there.
Aug
5
comment Reconstructing a morphism of exact triangles in the homotopy cat. of a dg-cat. using a “functorial cone map”
Sorry, I was being silly. I think tetrapharmakon is right actually, the space of maps $w$ as above should be contractible.
Aug
5
comment Reconstructing a morphism of exact triangles in the homotopy cat. of a dg-cat. using a “functorial cone map”
@tetrapharmakon, the problem is the other direction: given a map $w : C(f) \to C(f')$ as above, it is not necessarily induced by some $u$ and $v$.
Aug
3
awarded  Organizer
Aug
3
revised A model structure on marked simplicial sets
add tag higher-category-theory