From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory

This is a brilliant book. It explains the unexpected confluences and unifications of category theory as an extension of the Kleinian Erlangen program. It feels like the application of group transformations that "creates" space is simply setting out specific conditions generally without exception yields space. This to me is not merely an implication of theory to all potential practices, but the implicative order generated by the constraints of the transformations. How this avoids tautology and moves swiftly to show that various "complete" views are interchangeable, making them all party to a type of trivial pursuit makes me wonder whether it might not be better for the adoption of category theory into other fields of knowledge that the ultimate definition of morphism should not be changed to a chimera morphism. See, Efferman's Adjoint Functor paper. A chimera morphism at the very foundation of the theory then would have the conceptual seed to graph many analogies to ordinary and extraordinary phenomena. It would also make it easier, more convenient to accept that an asymmetric structure--the arrow--and its impetuous--is really about both "identity" [A is A] and difference [A is not-A]. Leibniz presumed such as core to his mathesis universalis. This intuition is captured and subsumed by the more general and inclusive f: A-> B.