https://incipit0.github.io/pweb/tags/maths/Recent content in Maths on [[logs]]Hugoen-usFri, 03 Nov 2023 19:53:38 +0000https://incipit0.github.io/pweb/posts/adjunctions/Fri, 03 Nov 2023 19:53:38 +0000https://incipit0.github.io/pweb/posts/adjunctions/<p>When I first encountered the concept of an adjunction, I got quite confused as to what it is, and why it is useful: Just how on earth is a left adjoint of a functor? What&rsquo;s the matter of a free and forgetful functor, why is free left to forgetful but not the other way round. That&rsquo;s where this blog comes from. I hope this blogpost can help demystify adjunction for you a little bit.</p>https://incipit0.github.io/pweb/posts/monad/Tue, 24 Oct 2023 23:48:44 +0100https://incipit0.github.io/pweb/posts/monad/A monoid in the category of monad tutorialshttps://incipit0.github.io/pweb/posts/fixpoint/Thu, 30 Jun 2022 08:59:42 +0100https://incipit0.github.io/pweb/posts/fixpoint/<p><a href="https://www.cl.cam.ac.uk/teaching/current/DenotSem/">Denotational Semantics</a> is a unique course offered by the Computer Lab at UoC. It can be intimidating at first glance but at the same time bring you lots of fun and frustration at the same time. In this blog post we will look at three proof techniques in domain theory and investigate the connections between them.</p> <p>In this blog we look at three techniques that can be used to prove the fixpoint of a function, namely, Tarski&rsquo;s fixpoint theorem, lfp1 + lfp2 and Scott induction. We will show that they are equivalent to each other by working on an example.</p>