Kerodon is an online textbook on categorical homotopy theory and related mathematics. It currently consists of a handful of chapters, but should grow (slowly) over time. It is modeled on …

An online resource for homotopy-coherent mathematics. $\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$ 1 Foundations Structure. Chapter 1: The …

An online resource for homotopy-coherent mathematics ... Kerodon $\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

1 The Language of $\infty $-Categories. A principal goal of algebraic topology is to understand topological spaces by means of algebraic and combinatorial invariants. Let us consider some …

An online resource for homotopy-coherent mathematics. We refer the reader to [] for a more detailed discussion (including an extension to the setting of topological groups).. Proof of …

Tags explained The tag system. Each tag refers to a unique item (section, lemma, theorem, etc.) in order for this project to be referenceable. These tags don't change even if the item moves …

2.4.3 The Homotopy Coherent Nerve. Let $\operatorname{Top}$ denote the category of topological spaces and let $\operatorname{N}_{\bullet }(\operatorname{Top})$ denote its …

An online resource for homotopy-coherent mathematics. 4.7 Size Conditions on $\infty $-Categories. Recall that a small category $\operatorname{\mathcal{C}}$ consists of the …

(see Remark 1.1.1.7).In §1.1.1, we prove a partial converse: from a collection of sets $\{ S_{n} \} $ and face operators $\{ d^{n}_{i}: S_{n} \rightarrow S_{n-1} \} $ which satisfy (), we can uniquely …

see Theorem 2.3.4.1.In other words, the formation of Duskin nerves induces a fully faithful embedding from the category $\operatorname{2Cat}_{\operatorname{ULax}}$ of Definition …