27 Oct 05:37 2014

### Double Dualization: Functions on vs. Figures in

Venkata Rayudu Posina <posinavrayudu <at> gmail.com>

2014-10-27 04:37:05 GMT

2014-10-27 04:37:05 GMT

Dear All, The constructs of GENERALIZED POINT (Sets for Mathematics, p. 150) and CONCRETE GENERAL (in the context of Functorial Semantics) are similar: (i) both are encountered in the course of getting to know a given object / graph / category; (ii) both begin with measurements (functions on [the given object] as opposed to figures in; Conceptual Mathematics, pp. 82-83); and (iii) both involve a two-step process i.e. double dualization. In light of these similarities, what exactly is the relation between generalized points A --> V (where A is a set of maps B --> V) and concrete generals A --> V (where A is a category of functors B --> V)? In other words, I'd appreciate any pointers to literature that explicitly brings functorial semantics to bear on physics (e.g. center of mass; Sets for Mathematics, p. 101). On a related note, one can get to know a given B by way of figures in B, instead of the above functions on B. Does the figures-and-incidence (Conceptual Mathematics, pp. 249-253) approach to knowing also involves two steps (like double dualization)? Can we think of modelling, for example, an irreflexive directed graph G as a parallel pair of functions source, target: Arrows --> Dots by way of taking points of map objects(Continue reading)