I’m experimenting here so hopefully the more mathematically knowledgeable among us won’t give me too hard a time. Perhaps one of the ways the argument of my previous post could be understood is in terms of mathematical categories. What mathematical categories allow us to think are functional morphisms or relations between sets. I’ll say more about this in a moment. In playful jab at my friend Nate, I wrote the following in my previous post:

Rhetorically Nate seems to think that it’s of no significance that his post was written on the internet, requiring fiber optic cables, a particular platform, news feeds, electricity, etc., that created the opportunity for our thoughts to be brought together and preserved despite the fact that we live an hour apart.

Drawing on the formal resources of category theory we can construct an external diagram of the point that I was trying to make, depicted in the upper lefthand corner of the post. In this diagram we notice that there are upper and lower case letters and arrows. The upper case letters are what are referred to as *objects* in category theory, and are essentially *sets*. Thus, for example, the set composed of Levi and Nate constitutes what category theory refers to as an *object* (not to be confused with what OOO refers to as an object). We can denote this set with the name “conversants” or communicants, or simple “C” for short. The lower case letters refer to rules defining relations, morphisms, transformations, or correlations *between* sets. The relation between f and g connected by a small circle (I can’t figure out how to make the symbol here) is referred to as a *composition* of functions or morphisms and is read “g following f”. Thus, if we follow the arrows we have X pointing to Y governed by the morphism f and we have Y pointing to Z governed by the morphism g. We note that there is an arrow pointing directly from X to Z with the composition of g and f (g circle f, read as g following f)) which is to be read as the composition of these two morphisms for the three objects or sets involved.

read on!

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