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bio website preschema.com
location Essen, Germany
age 23
visits member for 4 years, 10 months
seen 11 hours ago

1d
revised What is the Beilinson regulator?
update broken link
1d
suggested suggested edit on What is the Beilinson regulator?
Sep
27
answered Existence of ind-right adjoint functor for semi-simple category?
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.