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visits member for 4 years, 2 months
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Dec
3
comment What are some important examples of differential objects that aren't naturally graded?
I agree with Qiaochu's comment, however I think that it just hides the indices away in the category $\Delta$ which is defined combinatorially.
Sep
24
comment Quasi-isomorphism from “almost acyclic” complex to its homology
In fact, what does "$X$ is quasi-isomorphic to $Y$" mean?
Jun
20
comment On pushouts and mapping cylinders in exact categories
For the prospective reader, I might add that the easy observation that the forgetful functor from $C\mathcal N$ to the category of graded objects over $\mathcal N$ reflects exactness is implicitly being used.
Jun
17
comment On pushouts and mapping cylinders in exact categories
Great! In fact, not too many days ago I managed to solve the problem with help from my supervisor, and I was planning to post it here very soon. I got the same thing as you though I had to use elements to be convinced that the $P$ you define is effectively the pushout, etc. Thanks a lot for your effort on an already old and quite ignored question.
May
30
comment Is $\Omega \tilde X \simeq \Omega_0 X$?
Thanks! I'll eagerly read your expanded answer.
May
30
comment Is $\Omega \tilde X \simeq \Omega_0 X$?
Nice! I really like the argument, very clean. Didn't Milnor prove a theorem that loop spaces of CW-complexes have the homotopy type of a CW complex? (I didn't really ever read the actual formal statement), if that's the case then if $X$ is a CW-complex the proof works, and I'm interested in CW complexes so that's that :)
May
30
comment Is $\Omega \tilde X \simeq \Omega_0 X$?
Well ok, this is essentially the statement of the unique path lifting property, disregarding continuity issues, I think. What I still don't really get is why $\Omega_0$ appears.
May
21
comment showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels)
+1. This old answer of mine comes to mind.
May
16
comment Equivalent conditions for a preabelian category to be abelian
@t.b.: Almost three years later, I got to the point where I need to get into exact categories (as I seem to be getting into algebraic K-theory...) and your article seems to be the current standard reference. And it is a joy to read, your exposition is wonderful! It's sad that you don't hang around here anymore... Perhaps you will see this comment, and perhaps by the time you see it this question which shouts your name will have been answered already.
May
16
comment On pushouts and mapping cylinders in exact categories
Oh, I wish @t.b. wasn't "on extended leave" from the site...
May
14
comment What should a student (with algebraic-geometry minded) study in differential geometry?
Isn't just studying differential geometry good enough for every purpose? Just a thought.
May
8
comment Limit Creating Functor
What is the question?
May
3
comment In a Morita context ($A, B, P, Q, f, g$), why are $P$ and $Q$ projective if $f$ is surjective?
No problem. You can upvote if you think it's useful. If you have any more questions, post them here as a comment and I'll try to help out.
Apr
23
comment Question about Hopf-Rinow theorem
Have you checked do Carmo's "Riemannian geometry" book? The Hopf-Rinow theorem is there on pages 146-148, and he proves the equivalence of these two statements.
Apr
23
comment Question about Hopf-Rinow theorem
Does ANII mean "Axiom of Numerability number II"? Also, I don't see where the question is. Are you asking why those two statements are equivalent?
Apr
23
comment Suggestion about Algebraic Topology talk
You could look at R. Brown's "Topology and groupoids" book.
Apr
23
comment What is the suspension used in the Freudenthal suspension theorem?
@Rhoswyn: I think you are asking how to explicitly define $\Sigma f$ for an arrow $f$. I've included this in my answer.
Apr
23
comment What is the suspension used in the Freudenthal suspension theorem?
+1! I've expanded my answer to include some stuff that in particular explains how to obtain the suspension from two cones.
Apr
23
comment What is the suspension used in the Freudenthal suspension theorem?
You should remove the tag "fiber bundles"... They really don't appear in your question. Also, John is right (see my answer).
Apr
23
comment What is the suspension used in the Freudenthal suspension theorem?
Does this answer your question or is there something that you'd like me to expand?