I followed up a bit on my earlier post concerning the characterization of “structure.” Since I am now teaching a graduate seminar on structure in philosophy, mathematics, and physics, I actually read through a number of graduate textbooks in mathematics to figure out how it is defined in various branches of mathematics. And I produced a handout, summarizing the result. It can be found on the course website for the seminar. I would like to encourage readers to give their own definitions, or definitions they found elsewhere and found useful. The more the merrier!