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Homotopy theory, homological algebra, algebraic treatments of manifolds.

7
votes
I am not sure if this is the type of direct proof that you are looking for, but here it goes. I will start with a more general theorem: Let $M$ be a CANCELABLE monoid, and $K$ be the left adjoint to t …
answered Apr 14 '12 by Spice the Bird
11
votes
So this entire discussion is in Goerss and Jardine's "Simplicial homotopy theory" and also in May's "Simplicial objects in algebraic topology". Also Curtis' papers and monographs are very nice and cla …
answered Nov 10 '11 by Spice the Bird
4
votes
Here are some video lectures that John Morgan gave at Stony Brook http://www.math.sunysb.edu/Videos/dfest/ This also has many other nice mathematical videos.
answered Jul 20 '11 by Spice the Bird
2
votes
Their is a notion of a category that is homotopicaly small. These categories have a nerve that is well defined up to homotopy. The notion is as follows: Let $\mathcal{C}$ be a large category. It is ho …
answered Apr 6 '11 by Spice the Bird
1
vote
Any time you have a topological groupoid, you have a simplicial groupoid since geometric realization preserves finite limits. Although this seems like a rather trivial remark this allows for one to st …
answered Dec 26 '11 by Spice the Bird
11
votes
1answer
In Keven Walker's answer to the question, Cubical vs. simplicial singular homology it is written: Personally, I think it is more convenient to do singular homology with the larger collection …
asked May 23 '12 by Spice the Bird
34
votes
Showing that a certain number is equal to some infinite sum of numbers using power series. For example, showing that $\ln(2)=1-\frac{1}{2}+\frac{1}{3}-\cdots$ or $e=2+\frac{1}{2}+\frac{1}{3!}+\cdots$. …
answered Sep 2 '11 by Spice the Bird
5
votes
a mobius strip roller coaster. http://en.wikipedia.org/wiki/M%C3%B6bius_Loop_roller_coaster
answered Feb 13 '12 by Spice the Bird