We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

Every Elementary Higher Topos has a Natural Number Object

Formal Metadata

Title
Every Elementary Higher Topos has a Natural Number Object
Title of Series
Number of Parts
31
Author
Contributors
License
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
One key aspect of elementary topos theory is the existence of a natural number object. While it does not exist in every elementary topos (such as finite sets) we often need it to study more advanced aspects of topos theory (such as free monoids). In this talk we see how in the higher categorical setting, the existence of a natural number object can in fact be deduced from a small list of axioms that any reasonable definition of elementary higher topos should satisfy, hence proving that every elementary higher topos has a natural number object. We will observe how the proof involves ideas from algebraic topology, elementary topos theory and homotopy type theory.