I've been amiss from here since August, but only because I've been prolific somewhere else.
I’ve been posting on LocalCharts
Blog
On elements in category theory
Today I stumbled upon a quote by Lawvere: There has been for a long time the persistent myth that objects in a category are “opaque”, that there are only “indirect” ways of “getting inside” them, that for example the objects of a category of sets are “sets without elements”, and so on. The myth seems … Continue reading On elements in category theory
A complexity-taming thing
I've just read one of the best pieces of writing about the why of applied category theory I ever had the pleasure to read. I resonate so much with it that I want to copy it verbatim here: How can we gain the benefits of standardization, compositionality and generality? There is no one answer, ex[c]ept … Continue reading A complexity-taming thing
No, the Yoneda lemma doesn’t solve the problem of qualia.
Category theory is an extremely insightful subject but its generality, the plethora of structural heuristics it provides, as well as its apparent conceptual simplicity make it very prone to cargo-culting. And the Yoneda lemma, being one of the most prominent theorems in category theory and one a student encounters relatively early, is object of many … Continue reading No, the Yoneda lemma doesn’t solve the problem of qualia.
A personal prospect of categorical cybernetics
I'm in the business of categorical cybernetics. But what is it exactly? Jules Hedges coined the term some years ago (2019), after he had been working on compositional game theory for serveral years already. He moved to Glasgow the following year, and at the same time I moved there to start my PhD. In fact, … Continue reading A personal prospect of categorical cybernetics
The unreasonable effectiveness of social structures
Here's my take: social structures are the most impactful technology humans ever developed. Some might be already frowning. 'Social structures' does not even fall into what most people would probably call technology. After all, it has to be something concrete that, ideally, I can throw out of a window, no? According to the dictionary, technology … Continue reading The unreasonable effectiveness of social structures
Grrr(othendieck) fibrations
Last night I finally wrapped my head around a definition of fibration which has been confusing me for a while. I thought I'd know how it worked until I didn't, only to realize my confusion stemmed from the fact I was looking at two subtly different definitions which are nonetheless equivalent. This made me angry … Continue reading Grrr(othendieck) fibrations
Mathematicians don’t care about foundations
Many people seem to believe mathematicians work in non-constructive, non-structural, battered foundations because they love their Platonic realm and have a kink for AC and LEM. The reality is most mathematicians don't have a clue about foundations, they don't care, and happily work informally for all their lives. Case in point, mathematical foundations are a … Continue reading Mathematicians don’t care about foundations
Enriched categories for language models
Tai-Danae Bradley gave a very interesting talk today, for the series of Cats4AI lectures about the following paper, with the usual stellar insights and intuitions she's able to communicate. An Enriched Category Theory Of Language: From Syntax To Semantics, Tai-Danae Bradley, John Terilla, and Yiannis Vlassopoulos My understanding of the situation is the following (and … Continue reading Enriched categories for language models
Tips on learning how to write proofs
In mathematics, proofs are all the rage. I'm currently TAing a course on theory of computation, which is the most math many students have seen in the last four years, and definitely not high school style mathematics (i.e. 'shut up and calculate'). So I've been asked some tips on how to cope with proof writing … Continue reading Tips on learning how to write proofs
Optics in three acts
The following is the script of my latest MSP101 talk. It's supposed to be an overview of optics covering three different ways to construct them and reason about them. Most of it is devoted to the understanding of Tambara theory and the profunctor encoding, for personal reasons: it's the last way of thinking about optics … Continue reading Optics in three acts
Open cybernetic systems II: parametrised optics and agency
Last time, I described how optics can be a good formalism for feedback systems, i.e. systems whose dynamics happens in two stages (which I dubbed 'do' and 'propagate'), like the undertow on a beach. It often happens, in practice, that a system dynamics is not set in stone: someone can turn a knob and change the dynamics at will...
Open cybernetics systems I: feedback systems as optics
I coauthored my first two papers! [0] It's work I'm very excited about, and it actually tells a single story which I'd like to put together here, by sketching the bigger picture. Moreover, this is the same story behind my most recent talk, 'Games with players', so there's lots to talk about! The papers stand … Continue reading Open cybernetics systems I: feedback systems as optics
Differential forms, reverse derivatives and machine learning
I was recently trying to convince Bruno that covectors (in the form of differentials of functions) are the real deal in gradient descent, despite the misleading name and countless pictures showing little arrows pointing downhill.
Errata: symmetric Lawvere spaces
Sometime ago I wrote a blog post about symmetric Lawvere spaces. I'm here to correct a huge/tiny mistake.
General abstract nonsense. 