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. Forage Part 1: Foundations. Chapter 1: The Language of $\infty $-Categories; Chapter 2: Examples of $\infty $-Categories; Chapter 3: …

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

4.3.3 Joins of Simplicial Sets. Our next goal is to extend the join operation of Definition 4.3.2.1 to the setting of $\infty $-categories (and more general simplicial sets). We begin with a slightly …

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 …

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 …

(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 …

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 …

Kerodon $\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$ about; changes; recent comments; bibliography. next. statistics. comments (0) Part 1: Foundations Chapter 1: …

An online resource for homotopy-coherent mathematics. where $\operatorname{Fun}'( \operatorname{\mathcal{S}}, \operatorname{\mathcal{C}})$ denotes the full ...