9,208 reputation
12449
bio website personal.us.es/fmuro
location Seville, Spain
age
visits member for 4 years, 7 months
seen 1 hour ago

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
comment 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
comment The evaluation fibration of a transitive, effective topological group action
If the action is effective, it's a bijection.
Aug
28
comment 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
comment 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
comment 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
comment Can you detect homological dimensions from homology?
What do you mean by the homological/injective dimension of a chain complex?
Aug
24
comment $G$-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
comment Schwede-Shipley theorem for monoidal categories?
What theorem? They have more than one.
Aug
14
accepted Homotopy transfer in the opposite direction
Aug
14
comment Homotopy transfer in the opposite direction
$\prod$ instead of $\bigoplus$?
Aug
14
comment Homotopy transfer in the opposite direction
Would you mind to edit your answer so that I can accept it?
Aug
13
comment 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
comment 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
comment 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
comment 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?