AstrAlgo cWeb Vol. 2013 (1031) issue GOL X #1165
Michael Heather, Nick Rossiter
The topos as a category of categories of categories has the power to capture Aristotle’s nature of the World as a recursive macrocosmos –microcosmos structure that is not available in the set theory of Hilbert’s finitary mathematics. The full structure where Euclidean space in a relativistic space-time manifold is emerging as an extensional model of the formal topos that is a cartesian closed category composing a quantum reality. With the great advantage of hindsight we are able to identify may of the universal themes down through the ages as integral to and integrable in the closed cartesian category of the 21st century upgrade to the category of sets from the last century. This lecture takes an overview of some of the very many original ideas from the past that are to be found in category theory to enrich our understanding of the Universe in Process: some instances resolve long standing issues but others raise new very pertinent issues of modern day life that will need to be resolved by our civilization. Overall it demonstrates category theory as a natural formal language of a metaphysical reality for which our World is an instantiation.