This book provides an introduction to modern homotopy theory through the lens of higher
categories after Joyal and Lurie, giving access to methods used at the forefront of research …

The idea for this book was conceptualized during a research visit to Macquarie University in
the summer of 2017. At first, I was interested in collecting exotic examples of model …

In Part I of this thesis, we introduce algebraic model structures, a new context for homotopy
theory in which the cofibrations and fibrations are retracts of coalgebras for comonads and …

In a previous work, we have introduced a weakening of Quillen model categories called
weak model categories. They still allow all the usual constructions of model category theory …

We give an analysis of the non-constructivity of the following basic result: if X and Y are
simplicial sets and Y has the Kan extension property, then Y^ X also has the Kan extension …

The interpretation of types in intensional Martin-Löf type theory as spaces and their
equalities as paths leads to a surprising new view on the identity type: not only are higher …

We show that the category of algebraically cofibrant objects in a combinatorial and simplicial
model category A has a model structure that is left-induced from that on A. In particular it …

Categorical structures and their pseudomaps rarely form locally presentable 2-categories in
the sense of Cat-enriched category theory. However, we show that if the categorical …

We describe new structure on the Goodwillie derivatives of a functor, and we show how the
full Taylor tower of the functor can be recovered from this structure. This new structure takes …

The aim of this book is to introduce the basic aspects of the theory of∞-categories: a
homotopy theoretic variation on Category Theory, designed to implement the methods of …