Exploring mathematical objects from custom-tailored mathematical universes · HackerPapers discussionshttps://hackerpaper.kaipfister.de/p/2204.00948/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMTExploring mathematical objects from custom-tailored mathematical universes — mentioned by maxiepoohttps://news.ycombinator.com/item?id=35218958urn:hackerpapers:mention:2204.00948:35218958Sun, 19 Mar 2023 13:58:46 GMT<p>Basic results that are useful on a day-to-day basis: 1. Yoneda&#x27;s Lemma, and the corollary that objects defined by universal property are unique up to unique isomorphism 2. Right adjoints preserve limits and more generally, Kan extensions The &quot;big&quot; theorem of basic category theory is probably the adjoint functor theorems which, once you realize that so many constructions in math are adjoint functors, gives very useful technical conditions to construct such an adjoint (ctrl-s for &quot;applications&quot; here for examples: https://math.stackexchange.com/questions/844131/adjoint-func...). The most…</p><p><a href="https://hackerpaper.kaipfister.de/p/2204.00948/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.HO