Levels in the toposes of simplicial and cubical sets

Emily Riehl – 3 March 2010

In this talk, I hope to enlist the experts to help a non-expert help some former Macquarie students and visitors publicise their work. I will describe proofs due to Carolyn Kennett, Michael Zaks, and Michael Roy that answer a question of Bill Lawvere concerning a certain measure of the complexity of objects in a topos arising from the complete lattice of essential subtoposes. These results have been re-written-up and very slightly improved in a forthcoming paper on the topic. While I am confident about the arguments, I am less sure of the assertions made in my introduction, as my topos theoretic background is quite shocking. I hope that the audience's heckling will alert me in case I claim anything too ridiculous.