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Nov
25
answered K theory long exact sequence
Nov
23
comment Categorical or simplicial introduction to modern homotopy theory
For Blakers-Massey at least, there is a nice model independent proof described in a note of Rezk.
Nov
13
awarded  Custodian
Nov
13
reviewed Approve Irrationality of $ \pi e, \pi^{\pi}$ and $e^{\pi^2}$
Oct
31
comment Algebraic geometry introduction for homotopy theorists/algebraic topologists
At a more basic level, I think that the "functor of points" approach to algebraic geometry is much clearer to students comfortable with homotopy theory or category theory. So one might prefer to read something like Toen's course notes, before reading a scheme theory book.
Oct
30
awarded  Enlightened
Oct
30
awarded  Nice Answer
Oct
28
revised Geometric morphism of $\infty$ topos
deleted 1 character in body
Oct
28
answered Geometric morphism of $\infty$ topos
Oct
15
comment A tensor product for triangulated categories?
There is some discussion of this question in an old paper of Bondal-Larsen-Lunts (arXiv:math/0401009).
Oct
14
revised Is dgCat a category or a 2-category?
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Oct
14
comment Is dgCat a category or a 2-category?
Any model category (in fact, even just a category with weak equivalences) gives rise to an $(\infty,1)$-category. For example, if one takes simplicially enriched categories as a model of $(\infty,1)$-categories, this is given by the Dwyer-Kan simplicial localization.
Sep
29
comment Is dgCat a category or a 2-category?
@ZhenLin: Gepner-Haugseng show that the $\infty$-category of $V$-enriched $\infty$-categories has an enrichment over itself, for $V$ a presentably $E_2$-monoidal $\infty$-category. In particular this gives the enrichment of DGCat over itself, and hence via Dold-Kan an enrichment over $\infty$-categories. (I'm using implicitly the rectification result of Haugseng, which implies that DGCat is equivalent to the $\infty$-category of $\infty$-categories enriched over the $\infty$-category of chain complexes.)
Sep
29
answered Is dgCat a category or a 2-category?
Sep
27
awarded  Nice Answer
Sep
26
comment $E_{\infty}$ $R$-algebras vs commutative DG $R$-algebras vs simplicial commutative $R$-algebras
Yes, the functor $\phi$ just sends a simplicial algebra to its "normalized cochain complex".
Sep
26
answered Derived algebraic geometry: how to reach research level math?
Sep
23
comment Why do the model structures on dg-algebras and on dg-categories are not compatible?
A small remark: the functor of $\infty$-categories from (dg-algebras) to (dg-categories) factors through a functor to the $\infty$-category of pointed dg-categories which is fully faithful. As you point out, the mapping spaces in (pointed dg-categories) are obtained from the mapping spaces in (dg-categories) by quotienting out by the action of the simplicial group of units.
Sep
16
awarded  Nice Answer
Jun
26
awarded  Notable Question