bio | website | personal.us.es/fmuro |
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location | Seville, Spain | |
age | ||
visits | member for | 4 years, 7 months |
seen | 1 hour ago | |
stats | profile views | 6,003 |
I'm a mathematician interested in algebraic topology, category theory, homological algebra, and K-theory.
Sep
1 |
comment |
Relationship between $H_*(X, A)$ and $H_*(Y \cup_f X, Y)$? $\pi_*(X, A)$ and $\pi_*(Y \cup_f X, Y)$?
Start with the wedge of a circle and a sphere and then fill in the disk. |
Aug
31 |
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Injective model structure on sheaves of bounded complexes of $A$-modules
I think that, in all cases, cofibrations should be cochain maps which are mono in strictly positive degrees (not necessarily in degree $0$), so that the $t$-structure truncation functor from the unbounded category is a left Quillen functor. |
Aug
29 |
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The evaluation fibration of a transitive, effective topological group action
If the action is effective, it's a bijection. |
Aug
28 |
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Why do the model structures on dg-algebras and on dg-categories are not compatible?
It's also worth to say that $Map_{dg-cat}(\mathbf{k},\mathbf{B})$ is the classifying space of the topological/simplicial group of derived units in $\mathbf{B}$, i.e. $Map_{dg-algebras}(\mathbf{k}[t^{\pm1}],\mathbf{B})$. |
Aug
25 |
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About a (new?) definition of transformation (anti.transformation) as a link between natural and dinatural transformations
What you call anti-transformation is just a functor $\mathscr A\rightarrow\operatorname{Fact}(\mathscr C)$ to MacLane's twisted arrow category, a.k.a. Baues's category of factorisations $\operatorname{Fact}(\mathscr C)$ of $\mathscr C$, ncatlab.org/nlab/show/category+of+factorizations. |
Aug
24 |
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Can you detect homological dimensions from homology?
@WillSawin do you mean complexes of injective modules? By contrast, injective complexes are contractible, I think. |
Aug
24 |
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Can you detect homological dimensions from homology?
What do you mean by the homological/injective dimension of a chain complex? |
Aug
24 |
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$G$-CW complex structure of certain G-space
@Surojit so you complain that Mark Grant didn't answer a question you didn't pose? I think Mark's answer does answer your question. Maybe you should open a new thread if you have a new question. |
Aug
24 |
reviewed | Reject and Edit Fibered example of topologically slice knots |
Aug
24 |
revised |
Fibered example of topologically slice knots
grammar |
Aug
16 |
comment |
Schwede-Shipley theorem for monoidal categories?
@DavidWhite thanks! So maybe abc.xyz could restate the question saying that he's considering the category of modules over an $E_1$(resp. $E_2$)-algebra in the stable $\infty$-category of spectra. |
Aug
16 |
reviewed | Approve Socle of Almost Complete Intersections |
Aug
15 |
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Schwede-Shipley theorem for monoidal categories?
What theorem? They have more than one. |
Aug
14 |
accepted | Homotopy transfer in the opposite direction |
Aug
14 |
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Homotopy transfer in the opposite direction
$\prod$ instead of $\bigoplus$? |
Aug
14 |
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Homotopy transfer in the opposite direction
Would you mind to edit your answer so that I can accept it? |
Aug
13 |
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Homotopy transfer in the opposite direction
Trying to look for a more conceptual explanation, it looks like if it works because $\mathcal O_\infty$ is augmented and the endomorphism operad of $X$ is a non-unital suboperad of the endomorphism operad of $Y$, right? The inclusion of endomorphism operads being defined via the splitting. |
Aug
13 |
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Homotopy transfer in the opposite direction
Ok, that's theorem 10.3.7 in the published version. The proof is mistaken, if the argument were true any quasi-isomorphism should be injective! Actually, what I'm asking about would yield a proof of that theorem as a corollary (at least over a field), since any quasi-isomorphism between cofibrant complexes can be replaced with a roof of strong deformation retractions. |
Aug
13 |
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Why higher category theory?
There are many incarnations of higher category theory, but there's a particularly simple one: topological categories, i.e. categories whose morphism sets carry a natural topology. I'm sure you'll be able to come up with many examples of this. It's undeniable that they are ubiquitous in nature and deserve to be studied. |
Aug
13 |
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Homotopy transfer in the opposite direction
Hi Vladimir, I can't find any 10.3.12. I've tried to figure out what result you mean in that chapter without much success, maybe theorem 10.3.7? |