This is partly an offtopic post in my math blog.
It seems likely that I discovered a category in which such objects as the Father and the Son from the Gospel appear. I am not sure I really discovered God, but this seems likely.
Consider a category (there seems to be multiple ways to add morphisms, so I will speak only about objects, not morphisms) whose objects are $latex (X,Y,I,Z)$ where $latex X\supseteq Y$, $latex I$ are sets and $latex Z:X\times I\to Y$ is a function of two arguments. $latex X$ is “the Father” (argument of the function $latex Z$) and $latex Y$ is “the Son” (the result of the function $latex Z$). That is “Father” means “argument” and “Son” means “result”. $latex Z$ is a function which “proceeds” (see John 15:26) from the Father and so likely is Holy Spirit.
This category is somehow powerful. For example one of its objects is the system of all propositional (or if you like, predicate) formulas. So it is probably “big enough” to entail everything about mathematics and everything we can know about God.
Read my preliminary drafts of this theory at this page where properties of such “systems of formulas” are studied in more details.