The Topos of Virtuality

The Topos of Virtuality Part I: From the Neumann-Nave Topos to the Explication of Social Space

Generalizing the conceptual approach to a theory of biosemiotics which is primarily based on insight from mathematical topology 3 , we discuss here the relevance of the cognitive representation of the category of space in terms of the consequences implied by topos theory: In this sense, it is shown that a topos is a Lindenbaum-Tarski algebra for a logical theory whose models are the points of a...

THE INTERNAL IDEAL LATTICE IN THE TOPOS OF M-SETS

We believe that the study of the notions of universal algebra modelled in an arbitarry topos rather than in the category of sets provides a deeper understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6], [7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of a lattice L (in the category of sets) is an important ingredient of the categ...

The Creeping Virtuality of Place

Places are inherently dynamic. The boundaries of administrative regions (e.g., provinces and countries) and natural regions (e.g., coastlines, ecosystems, mountains, ice sheets, tectonic plates) can alter over time, as can their names. Cities have a daily influx and egress of people and vehicles, buildings go up and down, streets sometimes get repaired, added, etc. Even when a place persists, i...

The Virtuality of Territorial Borders

The Herbrand Topos

We define a new topos, the Herbrand topos, inspired by the modified realizability topos and our earlier work on Herbrand realizability. We also introduce the category of Herbrand assemblies and characterise these as the ¬¬-separated objects in the Herbrand topos. In addition, we show that the category of sets is included as the category of ¬¬-sheaves and prove that the inclusion functor preserv...