Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunction seeming to be the primary lens. Our topic is a theory showing “where adjoints come from”.
Brain Functors: A mathematical model of intentional perception and action
October 21, 2017 by
Semiadjunctions (essentially a formulation of universal mapping properties using hets) can be recombined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior).
The Joy of Hets (talk slides)
February 29, 2016 by
These are the slides from a talk on the role of heteromorphisms (hets) in category theory given at the Category Theory Seminar at NYU on January 13, 2016.
On Adjoint and Brain Functors
June 16, 2015 by
We give a heterodox treatment of adjoints using heteromorphisms (object-to-object morphisms between objects of different categories) that parses an adjunction into two separate parts (left and right representations of heteromorphisms). Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. This is a preprint of the paper coming out in Axiomathes.
Adjoints and Brain Functors
December 11, 2012 by
These slides define the potentially important notion of a brain functor which is a cognate of the notion of adjoint functors.