Category Theory For Beginners: Graphs And Dynamical Systems
In this video I discuss how we can make categories of structured sets (the category of graphs, and the category of dynamical systems, and the category of functions), by considering functors. In particular, I show how the category of functors from the category with two parallel arrows, to the category Set corresponds to the category of graphs. I illustrate how graph homomorphisms correspond to the natural transformations between such functors. I also describe the category of dynamical systems, and the category of functions using this idea. I also show that the category of dynamical systems is isomorphic to a subcategory of the category of functions, which in turn, is isomorphic to a subcategory of the category of graphs. Here I use the term "dynamical system", in the same loose sense as Lawvere does in his great book "Conceptual Mathematics", to just mean a function from a set to itself. Note that the kind of graphs we discuss are also called `quivers'.
https://en.wikipedia.org/wiki/Quiver_...)
This unlisted video describes how to find subobject classifiers in the kinds of functor categories I describe in this video, and may help people wishing to connect this material with my video on topos theory.
• Topos Theory: Finding subobject class...
Watch video Category Theory For Beginners: Graphs And Dynamical Systems online without registration, duration hours minute second in high quality. This video was added by user Richard Southwell 10 September 2019, don't forget to share it with your friends and acquaintances, it has been viewed on our site 6,752 once and liked it 197 people.