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Results tagged with motivation
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user 290
13
votes
Why localize spaces with respect to homology?
In particular, are there analogous constructions in ("cowardly old") algebra where we get something useful by formally inverting the maps inverted by some other functor?
Sure. Localize the catego …
- 118k
5
votes
How to motivate the skein relations?
Here is a sketch of how the skein relations appear in the approach to knot invariants based on braided monoidal categories coming e.g. from representations of quantum groups.
Suppose $V$ is a dualiz …
- 118k
10
votes
Commutative rings : Topoi = Fields :?
This is a long comment. I would prefer to say that (Grothendieck) topoi are "(some) affine schemes over $\text{Spec } \text{Set}$." Here is my preferred version of the table, sprinkle $\infty$s accord …
- 118k
20
votes
Why is the definition of the higher homotopy groups the "right one"?
There are many things to say here. Here's one. Suppose you want to classify all spaces up to (weak) homotopy equivalence, or equivalently all CW complexes up to homotopy equivalence. The zeroth step i …