$\infty$-topoi and Natural Phenomena: Generation

TL;DR

This paper demonstrates that the Segal topos of derived stacks over simplicial commutative algebras forms an $$-topos with a subobject classifier, providing a formal framework for modeling natural phenomena and generating dynamics.

Contribution

It establishes that the $$-category of derived stacks is an $$-topos with a subobject classifier, linking higher category theory to natural phenomena modeling.

Findings

The Segal topos of derived stacks has a subobject classifier.

The associated $$-category is an $$-topos.

Formalism of Higher topoi is applicable to natural phenomena modeling.

Abstract

We show that the Segal topos of derived stacks over simplicial commutative $k$-algebras, which can be used to model natural phenomena, has a subobject classifier, something we regard as being a source from which dynamics is generated. This is done by considering the $\infty$-category associated to such a Segal topos, which turns out to be an $\infty$-topos. At this point we have the formalism of Higher topoi at our disposal to deal with Higher Category Theory concepts in a transparent manner.