I am rereading rereading Robert Goldblatt’s book, Topoi, though in many respects it seems like I’m reading it for the first time. When there is enough time and space between myself and some volume or other, that experience of ‘(re)reading it for the first time’ is not all that uncommon. It occurred not too long ago with E.P. Thompson’s The Making of The English Working Class, and Durrell’s Alexandria Quartet. Those works both had in the neighborhood of forty years between the first and the second readings, so I feel less guilty at the sense of surprise and pleasure. With Topoi, my excuses are somewhat more thin, though I can still assert with considerable truth and honesty that there’s been considerable intellectual development on my part since the first time I tackled the book. I mention this not just to make what amounts to little more than a peculiar Facebook post (some people share pictures of their meal, after all), but to set up a discussion of why a Whiteheadian should pay special attention to that area of abstract algebraic thinking known as Category Theory. I’ll first spend a few words talking about the book itself.

The word “topoi” is the plural form of “topos,” which seems rather more elegant than saying “toposes.” A topos is a category theoretic structure that is rich in a variety of “nice” formal characteristics, the details of which I’ll spare you (as that would require an entire book on category theory to explain.) Now, a category (such as might take on the structural features that would further specify it to be a topos) is a mathematical constructions that turns away from “objects” so-called to devote particular attention to functions, transformations, and operations without any special concern for the supposed “what” that is being transformed or operated on. As such, category theory is arguably the purest form of algebraic thinking around. It is scarcely an accident that Leo Corry’s magnificent history of the development of abstract algebra, Modern Algebra and the Rise of Mathematical Structures, ends with the emergence of category theory.