Timeline for defining a bicategory of real-valued matrices
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2014 at 19:55 | comment | added | Adam Gal | One thing you can do is generalize relations by giving a function on the middle set (the one that maps to the ends) and then this corresponds to a morphim from functions on one set to functions on the other, so basically to this matrix. This can be generalized by replacing function with distribution, vector bundle, sheaf etc. | |
| Apr 1, 2014 at 2:25 | answer | added | Qiaochu Yuan | timeline score: 4 | |
| Mar 31, 2014 at 13:10 | comment | added | Zhen Lin | The $\mathbf{Poset}$-enrichment of $\mathbf{Rel}$ is coming from the fact that $\{ 0, 1 \}$ is itself partially ordered. Perhaps you might have better luck with a (tropical) semiring instead of a field? | |
| Mar 31, 2014 at 11:13 | comment | added | Noam Zeilberger | $\mathbf{FinMat}$ is a monoidal category, and so can be re-interpreted as a 2-category in the way you describe, but that just shifts my question one dimension up. Under that interpretation, each finite function $f : X \to Y$ determines a pair of linear transformations $k^{|X|} \to k^{|Y|}$ and $k^{|Y|} \to k^{|X|}$, and the question is whether/in what sense these can be seen as "adjoint"? | |
| Mar 31, 2014 at 10:40 | comment | added | Buschi Sergio | you can consider vector spaces with a fixed finite base, the tensor product as arrows and linear morphisms as cells, this is a classical module's bicategory type. | |
| Mar 31, 2014 at 7:49 | history | asked | Noam Zeilberger | CC BY-SA 3.0 |