Mario Román

This account is mostly inactive. Please do reach me via email :)

[Mario Román @mroman42]

@sarah_zrf Ooooh, I see, that's cool!

[Mario Román @mroman42]

@sarah_zrf Yay! Is this https://t.co/rgRWRGKXyP? I have the composition of lenses written there but can you do animations?

[julesh @_julesh_]

Mario Román (@mroman42) again - "Open diagrams via coend calculus". I **love** this stuff, and not only because it's useful for me - comb diagrams for open games are part of the motivation - the pictures are so pretty

[julesh @_julesh_]

Mario Román (aka @mroman42) - "Profunctor optics, a categorical update". Comprehensive work on optics that came out of last year's ACT school

Hopefully everyone was paying attention, this will be on the exam (in my talk tomorrow)

[Bartosz Milewski @BartoszMilewski]

What a nice surprise! Our paper "Profunctor Optics, a Categorical Update" has been accepted for a keynote at Applied Category Theory 2020. When I was first approached to mentor at the ACT 2019, I though I had nothing, and almost declined the offer. But the great team did it!

[julesh @_julesh_]

New preprint time! Games on graphs: A compositional approach, with Elena Di Lavore and @PawSob

The punchline: "Open games on open graphs" are strong monoidal functors from the category of open graphs ("syntax") to the category of open games ("semantics")
https://t.co/2bfCHvbof5

[Mario Román @mroman42]

@star_autonomy Both online editors (TikZiT, Mathcha) and then manually tweaking the tikz code later with the text editor. It takes a bit of patience and has some problems, but sometimes it is easier than pure tikz.

[Mario Román @mroman42]

@star_autonomy Hi, Nicolas! something that works is to let distributors compose to form sets of possible meanings; a point tracks one of them. The intuition in https://t.co/ZLO4u0gVU2 can be useful. There are variations on this. It is in progress; hopefully, we will have something written soon.

[Mario Román @mroman42]

@Nadrieril @_julesh_ This! I think I was assuming the monoidal to be a cartesian product so that forgetful preserves it and then EM -> C -> [Kl,Kl] is composition of strong monoidal functors.

[Mario Román @mroman42]

@_julesh_ I think we talked about this in Tallinn and the proposal was

∫{C ∈ EM} . EM(MS, C × MA) × Kl(UC ⋊ B, T)
≅
∫{C ∈ EM} . EM(MS, C) × EM(MS, MA) × Kl(UC ⋊ B, T)
≅
EM(MS, MA) × Kl(UMS ⋊ B, T)
≅
C(S,MA) × C(MS × B, MT)

Not sure if that is what you want; it is still subcat

[Mario Román @mroman42]

@8ryceClarke Thank you, Bryce! These things owe a lot to the work together with the ACT group :)

[Mario Román @mroman42]

Coends, graphically :)

For instance, this is how to compose a lens with a continuation.

[Mario Román @mroman42]

@sir_deenicus This is a coend, a particular kind of colimit. So, yes, in some sense, it is analogous; but it is not an integral (at least not in any obvious way). This is a nice intro to coend calculus here: https://t.co/lDnjxUus1u

[Mario Román @mroman42]

@coecke That is, one is a monoid, creating a bimonoid with the cartesian structure. But then we also have their adjoints.

[Mario Román @mroman42]

@coecke Black comonoid copies and discards white monoid (or any representable functor); black monoid copies and discards white comonoid (or any correpresentable). White-black monoids coincide iff C is cocartesian; white-black comonoids coincide iff C cartesian.

[Mario Román @mroman42]

@rwolffoot @PawSob I may be using notation that suggests squashing but it is not intended to mean squashing, 2-cells are still natural transformations.

[Mario Román @mroman42]

@_julesh_ The open boundaries are nodes in the monoidal bicategory of profunctors. Unlabelled structures are the monoidal product (white) and the comonoid structure lifted from Cat via Yoneda (black).

[Mario Román @mroman42]

Or actually computing what a cartesian lens is.

[Mario Román @mroman42]

Or composing lenses

[alexis.toumi @AlexisToumi]

Just released a new version of DisCoPy! https://t.co/EWgxnkjXce

A cool new feature is a drawing function which turns a diagram into TikZ code, ready to copy and paste in a LaTeX article. That's how I wanna draw all my diagrams from now on.

[Mario Román @mroman42]

@xgrommx Ends appear naturally here as natural transformations, but in principle, this is more suited for coends.

[Mario Román @mroman42]

@tangled_zans In this case, I am calling continuation just to a function embedded into Optic (!), and then using coends to describe optics.