4
$\begingroup$

(This question was originally directed to Simone Virili, referring to the answer https://mathoverflow.net/a/103840/2926, but could also be addressed to the greater community.)

I was wondering if you have any references for the definition you gave in this post: Is there a categorical treatment of dynamical systems?

I'm looking for a standard categorical treatment of discrete dynamical systems. I know you can give an abstract definition in terms of actions and groupoids but I like yours because it somehow preserves the 'feeling' of a DDS and I need that.

Thanks.

$\endgroup$
3

1 Answer 1

1
$\begingroup$

I am really sorry not to have seen this question until now. I do not have any standard reference for this point of view on dynamical systems.

On the other hand, what you can say is that the category of $\Gamma$-flows, say with $\Gamma$ a monoid (but you can allow more general things), on a category $\mathcal C$, is exactly the category of functors $Func(\Gamma, \mathcal C)$, where $\Gamma$ is considered as a category with one object.

So, even if the "dynamical" point of view is usually not present, most standard books in category theory study this kind of functor categories.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.