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(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.

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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.

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