Categories everywhere

Categories everywhere

[Michael Barr, Prof.]

I think it interesting to know that categories are now apparently used in Ramsey theory, one of the last places I would have expected it: https://arxiv.org/abs/1506.01221

Michael
[1506.01221] Categorical Constructions and the Ramsey Property<https://arxiv.org/abs/1506.01221>
It has become obvious in the recent development that the structural Ramsey property is a categorical property: it depends not only on the choice of objects, but also on the choice of morphisms involved. In this paper we explicitely put the Ramsey property and the dual Ramsey property in the context of categories of finite structures and investigate the invariance of these properties under some ...
arxiv.org



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Re: Categories everywhere

[Matias M]

It was a while ago but I believe it was R. F. C. Walters who showed me an
extended abstract of a talk that F. W. Lawvere gave at Braga in 2007. It
was entitled "Dynamics and Cohesion in Finite Toposes" and included Ramsey
theory as a topic to be clarified.
Greetings to all,
Matías.


El jue., 4 jun. 2020 a las 18:13, Matias M (<matias.menni@gmail.com>)
escribió:

> Subject: Categories everywhere
> From: Michael Barr, Prof. <barr.michael@mcgill.ca>
> Date: 2020-05-23 13:31:33 +0000
> Newsgroup: gmane.science.mathematics.categories
> Server: news.gmane.io
>
> I think it interesting to know that categories are now apparently used in
> Ramsey theory, one of the last places I would have expected it:
> https://arxiv.org/abs/1506.01221
>
> Michael
> [1506.01221] Categorical Constructions and the Ramsey Property<
> https://arxi=
> v.org/abs/1506.01221>
> It has become obvious in the recent development that the structural Ramsey
> =
> property is a categorical property: it depends not only on the choice of
> ob=
> jects, but also on the choice of morphisms involved. In this paper we
> expli=
> citely put the Ramsey property and the dual Ramsey property in the context
> =
> of categories of finite structures and investigate the invariance of these
> =
> properties under some ...
> arxiv.org
>
>

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