  1. This paper shows how the universals of category theory in mathematics
provide a model (in the Platonic Heaven of mathematics) for the
self-predicative strand of Plato's Theory of Forms as well as for the idea of a
"concrete universal" in Hegel and similar ideas of paradigmatic exemplars in
ordinary thought. 2. The paper also shows how the always-self-predicative
universals of category theory provide the "opposite bookend" to the
never-self-predicative universals of iterative set theory and thus that the
paradoxes arose from having one theory (e.g., Frege's Paradise) where
universals could be either self-predicative or non-self-predicative (instead of
being always one or the other). 3. Moreover the paper considers one of the most
important examples of self-predicative universals in pure mathematics, namely
adjoint functors or adjunctions. It gives a parsing of adjunctions into two
halves (left and right semi-adjunctions) using the heterodox notion of
heteromorphisms, and then shows that the parts can be recombined in a new way
to define the cognate-to-adjoints notion of a brain functor that provides an
abstract conceptual model of a brain. 4. Finally the paper argues that at least
one way category theory has foundational relevance is that it isolates the
universal concepts and structures that are important throughout mathematics.
