bio | website | math.uni-augsburg.de/alg |
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location | Augsburg, Germany | |
age | 40 | |
visits | member for | 5 years, 4 months |
seen | Mar 20 at 12:46 | |
stats | profile views | 1,081 |
Feb 4 |
comment |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
Insofar as every (left proper, combinatorial) model category is Quillen equivalent to a simplicial one, I would compare it to the fact that, for example, every monoidal category is equivalent to a strict one. So one could call a Quillen equivalent simplicial model category a strictification of the original model category. As in the case of monoidal categories, I think it also makes sense to study the non-strict versions (or presentations). So I can rephrase my question as follows: What is a good property that makes a model category Quillen equivalent to one enriched over $\mathrm{Joyal}$? |
Feb 4 |
comment |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
This is too strong for being what I would call a natural condition. Every homotopy category of a simplicial model category (one that is enriched over $\mathrm{Quillen}$) can easily be seen to be a closed module over $h\mathrm{Quillen}$. But the surprising (?) fact is that every (simplicial or not) model category's homotopy category is a closed module over $h\mathrm{Quillen}$. |
Feb 4 |
comment |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
Could you give me link to Hovey's definition of a Joyal-model category? |
Feb 4 |
comment |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
@Muro I didn't spell it out. Added it. |
Feb 4 |
revised |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
added 149 characters in body |
Feb 4 |
comment |
When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories?
@Muro You won't get the natural closed module structure over $h\mathrm{Joyal}$ in the case of $\mathrm{Joyal}$. |
Feb 4 |
asked | When are homotopy categories of model categories closed modules over the homotopy category of $(\infty, 1)$-categories? |
Dec 13 |
awarded | Nice Question |
Jul 2 |
awarded | Curious |
Dec 27 |
accepted | Is the ideal membership problem solvable for differential ideals? Is there a good notion of a Gröbner basis? |
Dec 26 |
comment |
Is the ideal membership problem solvable for differential ideals? Is there a good notion of a Gröbner basis?
The ring $\Omega$ is super-commutative; the generators $x_i$ are of degree $0$, the generators $dx_i$ are of degree $1$. There is just one differential operator, the derivative $d$ of degree $1$, which fulfills $d \circ d = 0$, that is $d(dx_i) = 0$. |
Dec 21 |
asked | Is the ideal membership problem solvable for differential ideals? Is there a good notion of a Gröbner basis? |
Dec 21 |
comment |
Axiomatization of locally compact Hausdorff spaces via compact subspaces
This answer has been helping me most as this gives me more than just rewriting the usual axiom (which is a basic exercise). |
Dec 21 |
accepted | Axiomatization of locally compact Hausdorff spaces via compact subspaces |
Nov 18 |
comment |
What is torsion in differential geometry intuitively?
Your geometric picture is right. |
Nov 16 |
awarded | Yearling |
Nov 6 |
asked | Axiomatization of locally compact Hausdorff spaces via compact subspaces |
Oct 20 |
revised |
Interpetation of torsion and curvature in terms of families of nearby geodesics
added 306 characters in body |
Oct 20 |
comment |
Interpetation of torsion and curvature in terms of families of nearby geodesics
That the geodesics (or the geodesic spray) only encode the affine connection up to torsion, that I know. But I don't think that it means that my question cannot be answered: even in the case of the Jacobi equation, which is on geodesic variation, the torsion enters. This is, of course, because the Jacobi equation talks about the acceleration of the distance between geodesics and the covariant derivative enters in this acceleration directly. I'll edit my question above to make it more clearly. |
Oct 19 |
accepted | Scalar curvature notion for Cartan connections |