# Contents * Automatic table of contents {: toc} This entry is about the text * Jacob Lurie, higher topos theory, [arXiv:math/0608040v4](http://arxiv.org/abs/math/0608040) This book has prerequisites: [[nLab:category theory]] (see also the exposition in appendix A.1), in particular [[nLab:realization and nerve]]. The reading strategy outlined here is approximately the following: * Start with appendix A.2. * Continue with the overview chapter 1. * Chapter 2 developes the theory of fibrations of simplicial sets.The aim of this are mainly three different concerns: * Establishing the $\infty$-Grothendieck construction: The type of fibrations accomplishing this are left/right fibrations (aka. fibrations in groupoids) and cartesian fibrations (aka. Grothendieck fibrations). * Preparing the Joyal model structure: This is a foundational topic; the fibrant objects of this model structure are precisely $/infty$-categories. The technical vehicle for this are anodyne maps. * Provide a foundations for a theory of $n$-categories, for any $n\le\infty$. For the well definedness of this notion minimal fibrations (a special kind of inner fibrations) are introduced. * Omit chapter 3. * The rest of the book is concerned with constructions which in most cases are proposed in chapter 2. So concentrate on the following important topics: * the Grothendieck construction (already in chapter 2) * the Yoneda lemma and presheaves * limits and colimits * ind-objects * adjoint functors * $\infty$-topoi ## A.2 Model categories [[HTT, A.2 model categories]] [[HTT, A. simplicial categories]] ## 1. An overview of higher category theory [[HTT, 1. an overview of higher category theory]] ## 2. Fibrations of simplicial sets [[HTT, fibrations of simplicial sets]] ## 4 Limits and colimits [[HTT, 4. limits and colimits]] ## 5 Presentable and accessible $\infty$-categories [[HTT, 5. presentable and accessible infinity-categories]] ## 6. $\infty$-Topoi [[HTT, 6. infinity-topoi]]