Deep learning, despite its remarkable achievements, is still a young field. Like the early
stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad …

The purpose of these notes is to give a categorical presentation/analysis of homotopy type
theory. The notes are incomplete as they stand (October 2017). The chapter on univalent …

The theory developed by Gambino and Kock, of polynomials over a locally cartesian closed
category E, is generalised for E just having pullbacks. The 2-categorical analogue of the …

The rules governing the essentially algebraic notion of a category with families have been
observed (independently) by Steve Awodey and Marcelo Fiore to precisely match those of a …

We develop the usage of certain type theories as specification languages for algebraic
theories and inductive types. We observe that the expressive power of dependent type …

We introduce contextads and the Ctx construction, unifying various structures and
constructions in category theory dealing with context and contextful arrows--comonads and …

We present two Dialectica-like constructions for models of intensional Martin-Löf type theory
based on Gödel's original Dialectica interpretation and the Diller-Nahm variant, bringing …

In this book, we aim to introduce the reader to a modern research perspective on the design
of “full-spectrum” dependent type theories. After studying this book, readers should be …

Grothendieck fibrations are fundamental in capturing the concept of dependency, notably in
categorical semantics of type theory and programming languages. A relevant instance are …

Polynomial functors are categorical structures used in a variety of applications across
theoretical computer science; for instance, in database theory, denotational semantics …