8,949 reputation
12447
bio website personal.us.es/fmuro
location Seville, Spain
age
visits member for 4 years, 3 months
seen 11 hours ago

I'm a mathematician interested in algebraic topology, category theory, homological algebra, and K-theory.


1d
revised Constants sheaves on an open subset
typo
Apr
17
comment Fiber bundle in smooth category and topological category
@IgorBelegradek the space $BG$ is not a manifold, right? What do you mean by a smooth map into it?
Apr
16
comment Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?
@MatthiasWendt suitably complicated may be $R=\mathbb Z$ and, in this case, if you impose complexes in $\mathcal B$ to consist of countable abelian groups, then $\mathcal B$ is essentially small. This concerns Adeel's comment below.
Apr
16
comment Maps to the group completion
@JohnKlein I meant it's necessary, of course the H-structure should be extendable to an A-infinity structure
Apr
14
revised Does Schatten-p (quasi-)norm satisfy the norm inequality for 0<p<1?
edited tags
Apr
13
comment Maps to the group completion
@QiaochuYuan it must be group-like
Apr
9
comment Noncommutative group of invertible ideals of a ring
@Aurel and John Voight, what's the field of fractions of a noncommutative ring?
Apr
8
comment Noncommutative group of invertible ideals of a ring
What's a fractional ideal at all in a noncommutative ring?
Apr
6
reviewed Approve Combinatorics problem involving counting the number of certain substrings
Apr
6
comment category theoretic approach to Sylow theorems and finite group theory?
Could you make precise what "category theoretic" means for you?
Apr
2
comment Cofiber sequence $A\vee A \to A \wedge A \to \bar{A}\wedge \bar{A}$ for a spectrum $A$
If such a cofiber sequence existed for $A=R=S$, we would have $S\vee S\cong S$, which is not true.
Mar
28
reviewed Reject Weak convergence in $W^{1,p}_0$
Mar
23
revised When are (weak) homotopy equivalence testable on open covers?
added 23 characters in body
Mar
23
answered When are (weak) homotopy equivalence testable on open covers?
Mar
17
comment What kind of ringed space $X$ has the property that a locally free sheaf is projective in Qcoh$(X)$?
Smooth manifolds.
Mar
13
comment proving the injectivity half of de Rham's theorem by construction in degrees other than $1$ and $n$
And that quote should date back to 1957. What would he think today of AT?
Mar
12
comment Dimension leaking in homology as opposed to homotopy
Seifert-van Kampen 'leaks' dimension since it is about dimensions $0$ and $1$. The fundamental groupoid $\Pi_1(X)$ should be compared to the truncations $t_{\leq n}C_*(X)$ of the (singular) chains, which also preserves homotopy push-outs (both functors preserve homotopy colimits in general).
Mar
12
answered Choice of fibrations is like a choice of a basis of a module
Mar
10
comment How to prove that any perfect complex on an affine scheme is strictly perfect?
I now realize of the absurdity of my second comments and the following one.
Mar
10
comment How to prove that any perfect complex on an affine scheme is strictly perfect?
@ZhaotingWei, I wasn't thinking of gluing, just on the fact that being trivial and being locally free are local properties (the second one for obvious reasons).