Topic: homotopy type theory

Marco Giustetto examines how synthetic higher category theory can extend the proof methods of homotopy type theory. Internal reasoning in an infinity-topos can establish classical results about spaces in a form suitable for machine verification. For the next categorical dimension, Riehl and Shulman introduced synthetic (infinity, 1)-categories: simplicial objects satisfying finitely many conditions, whose finiteness brings technical advantages. The talk considers the extension to (infinity, n)-categories, identifying which features of the n = 1 theory survive and which cannot generalize. The w

What are the parallels between Intuitionistic Mathematics and Neurophenomenology, and their implications for how we conceptualize Computation? Inspired by AA Cavia’s recently published ‘Logiciel’ and work with the OREL Cognition Futures Reading Group, I hope to connect these foundational innovations in Mathematics and Cognitive Science to show a path toward an intentional, ethical, and suitably complex computational future. First an historical survey of the development of the two fields from the perspective of their initiators, LEJ Brouwer and Francisco Varela. Then a folding in of advancemen