Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

2 Examples of $\infty $-Categories

Structure

  • Section 2.1: Monoidal Categories
    • Subsection 2.1.1: Nonunital Monoidal Categories
    • Subsection 2.1.2: Monoidal Categories
    • Subsection 2.1.3: Examples of Monoidal Categories
    • Subsection 2.1.4: Nonunital Monoidal Functors
    • Subsection 2.1.5: Lax Monoidal Functors
    • Subsection 2.1.6: Monoidal Functors
    • Subsection 2.1.7: Enriched Category Theory
  • Section 2.2: The Theory of $2$-Categories
    • Subsection 2.2.1: $2$-Categories
    • Subsection 2.2.2: Examples of $2$-Categories
    • Subsection 2.2.3: Opposite and Conjugate $2$-Categories
    • Subsection 2.2.4: Functors of $2$-Categories
    • Subsection 2.2.5: The Category of $2$-Categories
    • Subsection 2.2.6: Isomorphisms of $2$-Categories
    • Subsection 2.2.7: Strictly Unitary $2$-Categories
  • Section 2.3: The Duskin Nerve of a $2$-Category
    • Subsection 2.3.1: The Duskin Nerve
    • Subsection 2.3.2: From $2$-Categories to $\infty $-Categories
    • Subsection 2.3.3: Thin $2$-Simplices of a Duskin Nerve
    • Subsection 2.3.4: Recovering a $2$-Category from its Duskin Nerve
    • Subsection 2.3.5: Twisted Arrows and the Nerve of $\operatorname{Corr}(\operatorname{\mathcal{C}})^{\operatorname{c}}$
    • Subsection 2.3.6: The Duskin Nerve of a Strict $2$-Category
  • Section 2.4: Simplicial Categories
    • Subsection 2.4.1: Simplicial Enrichment
    • Subsection 2.4.2: Examples of Simplicial Categories
    • Subsection 2.4.3: The Homotopy Coherent Nerve
    • Subsection 2.4.4: The Path Category of a Simplicial Set
    • Subsection 2.4.5: From Simplicial Categories to $\infty $-Categories
    • Subsection 2.4.6: The Homotopy Category of a Simplicial Category