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Results tagged with homotopy-theory
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user 310
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
22
votes
Accepted
triangulated vs. dg/A-infinity
I don't really think that triangulated categories are abominable, but they certainly have their problems which are a result of having forgotten the higher homotopies. For instance, non-functoriality o …
- 1,980
14
votes
2
answers
956
views
Is there a constructive description of type in the p-local stable homotopy category?
The title pretty much sums it up - but let me give a little bit of background first.
In the p-local stable homotopy category (basically one localizes away the torsion spectra which are not p-torsion) …
- 15.4k
6
votes
Do the signs in Puppe sequences matter?
Basically my interpretation of Mariano's answer is as follows: one needs to be consistent with the signs in the Puppe sequence in order for the good properties one wants to hold (namely the mapping ax …
- 8,681
12
votes
Categories which are not compactly generated
One example is the following - suppose that $M$ is a non-compact connected manifold of dimension $\geq 1$. Then the unbounded derived category of chain complexes of sheaves of abelian groups on $M$ ha …
- 8,681
5
votes
How to think about model categories?
One can also view model structures as a solution to the problem of when is a localization of a category locally small. In other words when one wants to invert a collection of morphisms the morphisms i …
- 8,681
2
votes
Higher vanishing cycles
I wouldn't go as far as to say I understand, but what I get from it is the following:
One can roughly consider the vanishing cycles functor as coming from gluing data for the recollement associated to …
- 8,681