# cate (blogs) — RSS Amplifier Recent posts from the 2 feeds in the RSS Amplifier directory that cover cate. Page: Feed: --- ## [(untitled)](https://aethy.com/@abuseofnotation/117127397565323832) _2026-08-20 · Abuse of Notation bot_ The order example with the number dividers is also isomorphic to an inclusion order, namely the inclusion order of all possible sets of prime numbers, including repeating ones (or alternatively the set of all prime powers). This is confirmed by the fundamental theory of arithmetic, which states that every number can be written as a product of primes in exactly one way. -- https://… ## [(untitled)](https://aethy.com/@abuseofnotation/117121926308419389) _2026-08-19 · Abuse of Notation bot_ I responded immediately “OK, you mentioned that it (the moon) wasn’t quite full, right. But which side was flat? If it is the left side, then this means that it is growing, which means that it will be full tomorrow or the day after, if this is so, then I will come with you.”: -- https:// abuseofnotation.github.io/mind -against-the-machine/confusion-breeds-clarity/06-outside/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/117115214610135552) _2026-08-18 · Abuse of Notation bot_ But we know already that $f$ and $f’$ are isomorphic and hence $fcirc f’ = id$, so the above formula is equivalent to (you can reference the diagram to see what that means): -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/01\_set/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/117109061072506410) _2026-08-17 · Abuse of Notation bot_ What’s even more amazing, is that we can define all of set-theory, based just on the concept of functions, as discovered by the category theory pioneer Francis William Lawvere. -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/02\_category/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/117103439263769084) _2026-08-16 · Abuse of Notation bot_ But I guess the masturbation metaphor isn’t quite accurate, as the only real purpose of these explanations manifested itself only when they were shared with other people, and only insofar as they were recognized by them (what makes mathematics so useful was that it had this property that anyone who is sucked deep enough in it would be completely unable to reject any of its fundaments). The issue… ## [(untitled)](https://aethy.com/@abuseofnotation/117075147405187755) _2026-08-11 · Abuse of Notation bot_ “We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies… ## [(untitled)](https://aethy.com/@abuseofnotation/117071199104293673) _2026-08-10 · Abuse of Notation bot_ The category of Limitation is often misunderstood because this triad is based on truth. Classical logic is bivalent: propositions are either true or false, yet this triad of quality has three categories. So, what is the third? -- https:// abuseofnotation.github.io/univ ersal-knowledge/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/117061309323918702) _2026-08-08 · Abuse of Notation bot_ We haven’t covered product categories, however some pages ago, when we covered monoids and groups, we talked about the concept of a product group. The good news is that product categories are a generalization of product groups… -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/11\_natural\_transformations/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/117032774038001792) _2026-08-03 · Abuse of Notation bot_ Many, if not most, of the of the things that we said about space, can also be said about time. Like space, it is universal and unique - we can only perceive one timeline, that is, for every two events we can always say that one comes before the other. Space and time are the two components that shape our reality - space allows objects to co-exist, and time enables their states to form a succession… ## [(untitled)](https://aethy.com/@abuseofnotation/117020100800025357) _2026-08-01 · Abuse of Notation bot_ Aside from facilitating code reuse by bringing in all standard functions of simple types in a more complex context, map allows us to work in a way that is predictable, courtesy of the functor laws, which in programming context look like this. -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/10\_functors/index.html ## [AI QA That Opens Fix PRs (Sponsored)](https://crawlproof.com/a/qIvu55SPh4Sw) _2026-08-01 · **Sponsored**_ Runs browser QA, files issues with repro evidence, and opens fix PRs. ## [(untitled)](https://aethy.com/@abuseofnotation/117007107538376684) _2026-07-30 · Abuse of Notation bot_ In deterministic systems, non-deterministic events can only be explained by “hidden variables” theories. These theories posit that any failure to predict an outcome is due to a lack of knowledge or understanding. While it is good stance to adopt for evolutionary reasons, as it drives us to analyze and systematize our surroundings, it becomes problematic when we take it too seriously. -- https://… ## [(untitled)](https://aethy.com/@abuseofnotation/117002900724303166) _2026-07-29 · Abuse of Notation bot_ Of course, he came to talk about work. Mirko would never come to me for any other reason. He started briefing me about the situation he was in with his current project. The whole story was very convoluted and I was absent-mindedly waiting to hear when he would start telling me how all this was related to the stuff I was working on. But that moment never came. After a couple of minutes he stopped… ## [(untitled)](https://aethy.com/@abuseofnotation/116987353133084824) _2026-07-26 · Abuse of Notation bot_ In contrast, intuitionistic logic represents the opposite view, that knowledge is subjective and limited in scope. Here, rather than contrasting reality with limitation, we use negation. A thing may be B or it may not be B, but it doesn’t have to be one or the other, because, since the predicate B is made up, there is no reason to think that it should apply to every object in the universe. This is… ## [(untitled)](https://aethy.com/@abuseofnotation/116981988912200162) _2026-07-25 · Abuse of Notation bot_ 3. At stage 2, we can make random observations or discard observations as they lose relevance. At stage 3, however, every observation must connect with all the other ones (it is this connection which is necessary). New observations must align with our worldview, and we cannot disregard established observations without impacting our entire conceptual structure. -- https://… ## [(untitled)](https://aethy.com/@abuseofnotation/116975113548416787) _2026-07-24 · Abuse of Notation bot_ 1. At stage 1 and 2, we operate on a phenomenological level, dealing only with things we directly perceive. In stage 3, however, we extend to imagining entities and concepts based on what we perceive but which cannot be directly observed. -- https:// abuseofnotation.github.io/univ ersal-knowledge/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/116965099032078355) _2026-07-22 · Abuse of Notation bot_ To keep the suspense, before we discuss the relationship between monoids and categories, we are going through see some simple examples of monoids. -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/03\_monoid/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/116959336758572412) _2026-07-21 · Abuse of Notation bot_ Realize how ridiculous this looks in the grand schema of things: someone comes up with marvelous new technology that solves all your issues and your first reaction as a society is “but what would the people who used to work on that issue do for a living?” -- https:// abuseofnotation.github.io/capi talism-innovation/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/116953452238258007) _2026-07-20 · Abuse of Notation bot_ Like we said at the beginning, with isomorphisms, going back and forth brings us to the same object, while with equivalence the object is just isomorphic to the original one. This is truly all there is to it. -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/11\_natural\_transformations/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/116946446876212313) _2026-07-19 · Abuse of Notation bot_ This is probably the most important example you will see if you want to understand what is FP all about. Not all functions can really be represented as data structures (many of them have infinite inputs), but all of them can be reasoned about as such. One way to grasp the power of this concept is to imagine how the function-data isomorphism scales. Imagine a simple function like the one you see… ## [(untitled)](https://aethy.com/@abuseofnotation/116946205253283626) _2026-07-19 · Abuse of Notation bot_ This particular equivalence (a set as a category with no morphisms) is, however, rarely useful. Not because it’s incorrect in any way, but rather because category theory is all about the morphisms — if the arrows in set theory are nothing but a connection between the sets that serve as their source and a destination, in category theory it’s the objects that are nothing but a source and destination… ## [Sync Bookmarks Everywhere (Sponsored)](https://crawlproof.com/a/BhweghkasQIz) _2026-07-19 · **Sponsored**_ Two-way sync keeps folders and toolbar intact across Chrome, Firefox, and Safari. ## [(untitled)](https://aethy.com/@abuseofnotation/116942439242628018) _2026-07-18 · Abuse of Notation bot_ Task 7: Try to extend the natural transformation in the other direction (by taking $baralpha$ to be identity). -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/11\_natural\_transformations/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/116939361554200013) _2026-07-18 · Abuse of Notation bot_ Unlike all other categories, the categories of modality are not concerned with the observed phenomena (objects, appearances etc.) but with the observer. This is why Kant says that they are not objectively synthetic (as all other categories), but it’s subjectively synthetic. -- https:// abuseofnotation.github.io/pure -reason/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/116933739199859665) _2026-07-17 · Abuse of Notation bot_ Like with categories, the object mapping of an order is represented by a function between the orders’ underlying sets. -- https:// abuseofnotation.github.io/cate gory-theory-illustrated/10\_functors/index.html ## [(untitled)](https://aethy.com/@abuseofnotation/116930905635616622) _2026-07-16 · Abuse of Notation bot_ By the way, the way Elon acts provides for me an irrefutable, proof that capitalism is dead — if the world’s richest person cannot just use their money to enjoy themselves and instead prefers to continually make a fool of themself and be ridiculed by the whole world on a daily basis, then what’s the point of it all? -- https:// abuseofnotation.github.io/elon -capitalism/index.html ## [America at 250: The Emmett Till of Chapel Hill](https://stonewalls.substack.com/p/emmett-till-of-chapel-hill) _2026-07-01 · Mike Ogle · Stone Walls_ A journey into our obstructed histories