La flèche du temps dans la théorie des catégories

http://panmere.com/?p=100

Dans Cat :

https://golem.ph.utexas.edu/category/2009/11/the_arrow_of_time_in_cat.html#more

ainsi que dans un commentaire de John Baez à cet article :

https://golem.ph.utexas.edu/category/2009/06/kan_lifts.html#c024719

« I’m glad you mentioned this, because it gives me an opening to say what I think causes the asymmetry that David’s interested in.

It’s the arrow of time!

Why is
Set
so different than
Set
op
? It’s because the morphisms are functions: relations that can be many-to-one, but not one-to-many.

Why do many-to-one but not one-to-many relations get singled out for single treatment and dubbed ‘functions’? Because functions are supposed to be ‘deterministic’: the cause must determine the effect. We don’t care if the effect fails to determine the cause.

Why does our customary concept of determinism have this asymmetry built in? Well, we see it a lot in ordinary life. It’s often (though not always) true that the initial state of an experiment determines the final outcome. But it’s much less common for the final outcome to determine the initial state… at least, not in an easily visible way.« 

Les « dagger -categories «  sont un cadre formidable pour le formalisme de la théorie quantique:

https://ncatlab.org/nlab/show/dagger+category

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