I find it convenient to think about persistence in terms of category theory. I will explain why this is natural, and how it simplifies my thinking. Sometimes it gives access to deeper theorems, and more often it is a tidy language that expresses just what I need. Examples will include: sublevelset and interlevelset homology; merge trees and Reeb graphs; generalized factor persistence; a fractional category for "physically measurable" persistent features; comparison theorems for Cech and Rips complexes. I thank my collaborators in these projects: Peter Bubenik, Gunnar Carlsson, Fred Chazal, Bill Crawley-Boevey, Marc Glisse, Dmitriy Morozov, Liz Munch, Vidit Nanda, Steve Oudot, Amit Patel, Jonathan Scott.