Category Theory Representables

Summary

We start by recapping Kan extensions. Next we cover free cocompletion and Yoneda extensions. We show how these ideas give ... We use the running example of the natural number object as the universal dynamical system to illustrate how Please watch with subtitles. Errata noted in transcript and at bottom of description. Some content may require a little background in ... Remember when I used a video with a coconut in the thumbnail to drive a stake through the heart of mathematical structure? A finite-dimensional vector space is isomorphic to its dual, but only if you pick a basis. It's also isomorphic to its double dual, and ... In this video we state and prove the Yoneda Lemma, and give examples of it in action within the sources and references, in temporal order: Nature paper on the decline in disruptive science: ... Can higher mathematics explain the structure of reality? In this episode of Know Time, mathematical physicist Urs Schreiber ... A gentle introduction to the study of We introduce fibrations intuitively by starting with discrete op fibrations. We describe connections and applications involving the ...