18.095 Lecture Notes - Lecture 3: Smoothness
Document Summary
David spivak a category-theoretic approach to understanding the steady states of coupled dynamic systems. Information is coupled, meaning it is owing from one into another. Averages are not compositional, but weighted averages are. Two types are dynamical systems that we will be focusing on are continuous and discrete. A space s = r , points are called states. A smooth function from s ts, meaning a vector eld on s, called the update function. Note, if a = r and b = r are euclidean spaces, an (a-b) continuous dynamical system calls for a vector eld on s to be parameterized by a. If a and b are sets, an (a-b) discrete dynamical systems consists of the following. A set s, elements of which are called states. A function a x s s calls the update function. A function that takes the state s and returns a readout b.
