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julesh.mathstodon.xyz.ap.brid.gy
julesh
@julesh.mathstodon.xyz.ap.brid.gy
250 followers 0 following 960 posts
Applied Compositional Thinking

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julesh.mathstodon.xyz.ap.brid.gy
I'm very sorry to lower the tone, but this title did literally make me do a double take
https://arxiv.org/abs/2503.10963
[Submitted on 14 Mar 2025] A study of Kock's fat Delta Tom de Jong, Nicolai Kraus, Simona Paoli, Stiéphen Pradal Motivated by the study of weak identity structures in higher category theory we explore the fat Delta category, a modification of the simplex category introduced by J. Kock. We provide a comprehensive study of fat Delta via the theory of monads with arities, and use these results to show that fat Delta is a hypermoment category in the sense of C. Berger. Specifically, by proving that the free relative semicategory monad is strongly cartesian and identifying a dense generator, the theory of monads with arities immediately gives rise to the nerve theorem. We characterise the essential image of the nerve via the Segal condition, and show that fat Delta possesses an active-inert factorisation system. Building on these results, we also establish an isomorphism between two presentations of fat Delta and show that it is a strongly unital and extensional hypermoment category.
November 16, 2025 at 4:42 PM
julesh.mathstodon.xyz.ap.brid.gy
Kleenex star
Kleene : Cont -> Cont Kleene a = Fix (\x => Plus I (Seq a x)) Kleenex : Cont -> Cont Kleenex a = Fix (\x => Plus I (Seq x a))
November 10, 2025 at 11:17 PM
julesh.mathstodon.xyz.ap.brid.gy
Ah yes, the Fourier Methodology in software engineering
Pooh meme Vibe check Vibration inquiry Fourier analysis
November 9, 2025 at 11:47 AM
julesh.mathstodon.xyz.ap.brid.gy
@christianp Argh, the Android client I use (Moshidon) already supported quote-tweets...... but not in a compatible way 😭
November 8, 2025 at 11:43 AM
julesh.mathstodon.xyz.ap.brid.gy
https://julesh.com/ is finally starting to look close to how I would like, after changing the font to Open Sans 3
November 2, 2025 at 12:28 PM
julesh.mathstodon.xyz.ap.brid.gy
Oh, I've been spelling it "adaptors" for years, and only just realised it was meant to be "adapters"
https://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/poptics.pdf
2.1 Adapters When the component being viewed through a lens is actually the whole of the structure, then the lens is essentially a pair of functions of types S → A and B → T; there is no virtue in the update function taking the old S value as an argument as well, because this will be completely overwritten. Dually, when the variant being accessed through a prism is actually the sole variant, the prism is again essentially a pair of functions of types S → A and B → T; there is no virtue in the matching function having a fallback option, because the match will always succeed. This is illustrated in Figure 2. We introduce an abstraction for such a pair of functions, which we call an adapter. data Adapter a b s t = Adapter {from :: s → a, to :: b → t} It is often the case that from and to are in some sense each other’s inverses; but we will not attempt to enforce that property, nor shall we depend on it.
October 29, 2025 at 5:47 PM
julesh.mathstodon.xyz.ap.brid.gy
Possibly the worst notational crime I have ever considered committing: last week I was writing ∘ with a subscript ∫ for "Chapman-Kolmogorov composition" of Markov kernels
https://en.wikipedia.org/wiki/Chapman%E2%80%93Kolmogorov_equation
but I found that quite […]

[Original post on mathstodon.xyz]
October 29, 2025 at 2:46 PM
julesh.mathstodon.xyz.ap.brid.gy
I've been a Firefox user for something like 15 years, and I have very high standards for a browser. I gave @zenbrowser a *very* thorough trial period running alongside Firefox for a month. In the end, I have decided to keep it and move fully away from Firefox […]

[Original post on mathstodon.xyz]
Screenshot of my Mastodon profile in Zen
October 26, 2025 at 11:26 AM
julesh.mathstodon.xyz.ap.brid.gy
More basic theory of "cartesian colinks", ie. lenses in a finite product category: the fibration structure, the tensor product, and the fundamental functors
https://julesh.com/forest/000A/index.xml
October 25, 2025 at 5:21 PM
julesh.mathstodon.xyz.ap.brid.gy
Hm, I just remembered that coslice categories do also exist so I really should not use the standard notation for them for the simple slice. I tried and failed to make Jacobs' notation C//X look good in KaTeX. Another option would be to call it C[X], which is […]

[Original post on mathstodon.xyz]
October 24, 2025 at 10:14 PM
julesh.mathstodon.xyz.ap.brid.gy
I have finally settled a very minor confusion I've had for many years: functions lift covariantly to morphisms of reader comonads but contravariantly to functors between their kleisli categories. It works out because comonad morphisms also lift […]

[Original post on mathstodon.xyz]
October 24, 2025 at 10:09 PM
julesh.mathstodon.xyz.ap.brid.gy
Ok that's enough baby stuff, time for some deeper folklore: notes on simple slice categories
https://julesh.com/forest/000F/index.xml
October 24, 2025 at 10:07 PM
julesh.mathstodon.xyz.ap.brid.gy
@dpiponi
We demonstrated quantum advantage! Sure, grandma, let's get you to bed
October 22, 2025 at 6:43 PM
julesh.mathstodon.xyz.ap.brid.gy
Here's something I twote about the last time the orange guy was in charge, this time I went to see it in real life. This window in St Giles' Cathedral, which looks like joke anachronism but is actually real, depicts the first ever assassination of a head of […]

[Original post on mathstodon.xyz]
October 22, 2025 at 5:11 PM
julesh.mathstodon.xyz.ap.brid.gy
"Please note that this machine is not a Tesla coil. If this machine starts behaving like a Tesla coil, you are having a bad day."
October 22, 2025 at 4:03 PM
julesh.mathstodon.xyz.ap.brid.gy
Liminal space in the National Museum of Scotland
October 22, 2025 at 3:16 PM
julesh.mathstodon.xyz.ap.brid.gy
This is a device for making briole cuirée, a fancy desert
October 22, 2025 at 3:11 PM
julesh.mathstodon.xyz.ap.brid.gy
The winner is Idris, by the way. I had to switch off dynamic shadows to push Minecraft above 20fps, but only the Idris typechecker is powerful enough to bring my entire operating system below 1fps
October 21, 2025 at 4:38 PM
julesh.mathstodon.xyz.ap.brid.gy
I used used a functor to create a "recent posts" list on my homepage, is this applied category theory?
October 19, 2025 at 3:55 PM
julesh.mathstodon.xyz.ap.brid.gy
Big shoutout to the community of people who could be developing better ballistic missiles or earning a fortune as quants but instead are saving frames in super mario 64 tool assisted speedruns

https://www.youtube.com/watch?v=_yx0eutBwII
October 18, 2025 at 7:54 PM
julesh.mathstodon.xyz.ap.brid.gy
*Much* better
October 18, 2025 at 2:11 PM
julesh.mathstodon.xyz.ap.brid.gy
This is what I'm up against:
https://julesh.com/posts/2024-02-22-iteration-optics.html
October 18, 2025 at 2:02 PM
julesh.mathstodon.xyz.ap.brid.gy
A website with good minimalist design (Forester) running on a web browser with good minimalist design (Zen) combine to make quite a vibe
October 16, 2025 at 10:22 PM
julesh.mathstodon.xyz.ap.brid.gy
Personally I think it would be more appropriate if Birmingham New Street Station was renamed Crazy Train Station
Sharon Osbourne has said it "would be amazing" if Birmingham Airport was renamed in honour of her late husband, rock legend Ozzy Osbourne. The TV personality has given her support to a campaign to call the airport Ozzy Osbourne International, which was launched by podcaster and comedian Dan Hudson after the Black Sabbath singer died at the age of 76 in July.
October 16, 2025 at 8:06 PM
julesh.mathstodon.xyz.ap.brid.gy
I just looked for the first time in years by the blog post that both Kmett and me credited with the reinvention of lenses in functional programming, and remembered that it does not in fact contain the definition of lenses

I thought it would be very funny to […]

[Original post on mathstodon.xyz]
data Accessor a = Accessor { readVal :: Game a , writeVal :: a -> Game () }
October 16, 2025 at 7:14 PM