I finally created a custom, fully static, self-hosted website, and bought a new domain! https://matteocapucci.eu/ If you are following my blog, you might want to switch to that. Go here and look for the new RSS feed link.
Moved to https://matteocapucci.eu/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. … Continue reading On elements in category theory →
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 →
Moved to https://matteocapucci.eu/no-the-yoneda-lemma-doesnt-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 … Continue reading No, the Yoneda lemma doesn’t solve the problem of qualia. →
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 →
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 →
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 →
Moved to https://matteocapucci.eu/mathematicians-dont-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 … Continue reading Mathematicians don’t care about foundations →
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. My understanding of the situation is the following (and I hope she’ll correct me if I’m wrong). At a first approximation, a language model (LM) learns … Continue reading Enriched categories for language models →