Synthetic category theory and type theory
This page aims to explain how type theory can be understood within the framework of synthetic category theory. The content of this page is derived from my questions to Tashi during the second exercise class and Tashi’s responses. I would like to express my gratitude to Tashi here. We focus on the following two questions: Question I. How should we understand the notion of isofibration (hereafter referred to as a fibration) in synthetic category theory? Question II. Do we still have a weak factorization system in this context? Next, we will answer these questions through the lens of type theory and the categorical perspective of synthetic category theory. ...