Timeline for Category Theory and Ergodic Theory
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2012 at 14:53 | comment | added | Esfan Haghverdi | Thanks, that is very helpful. In the past I did some work generalizing the partially additive categories (PAC) of Manes and Arbib to what I called Unique Decomposition Categories. The motivatuion for Manes and Arbib was of course to offer an algebraic denotational semantics as opposed to domain theoretic one of Scott. Each PAC is endowed with an iteration operator called dagger where given $f: X \to X\uplus Y$, $\dagger(f): X \to Y$ is given by $\sum_n f_2f_1^n$ where the sum is a partially defined infinitary operation on the homsets. I will look at these again in the light of your posts. | |
| Jan 21, 2012 at 14:44 | comment | added | Tom Leinster | As far as I was concerned, the idea was more to understand infinite iteration in a general setting, or to put my finger on what a "dynamical concept" is. I certainly wouldn't claim to have done so, but that's what was motivating me. | |
| Jan 21, 2012 at 14:40 | comment | added | Esfan Haghverdi | Thanks for the pointer. Even though after a cursory look I think the goal of the post is to understand a categorical phenomenon, namely the fact that an epi or mono endomorphism in certain categories (eg. locally finite ones) but also in the category of finite dimensional vector spaces is an iso, nevertheless it is a good starting point to reformulate more dynamical systems notions in categorical language and use them to solve a category theoretic problem. | |
| Jan 21, 2012 at 14:36 | vote | accept | Esfan Haghverdi | ||
| Jan 21, 2012 at 15:05 | |||||
| Jan 20, 2012 at 21:59 | history | answered | Moshe | CC BY-SA 3.0 |