Kerodon

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

5 The $\infty $-Category of Spaces

Structure

  • Section 5.1: Fibers of Left and Right Fibrations
    • Subsection 5.1.1: Covariant Transport
    • Subsection 5.1.2: A Characterization of Kan Fibrations
    • Subsection 5.1.3: Relative Homotopy Equivalences
    • Subsection 5.1.4: Covariant and Contravariant Equivalences
  • Section 5.2: Morphism Spaces
    • Subsection 5.2.1: Morphism Spaces
    • Subsection 5.2.2: Fully Faithful and Essentially Surjective Functors
    • Subsection 5.2.3: Digression: Categorical Mapping Cylinders
    • Subsection 5.2.4: The Comma Construction
    • Subsection 5.2.5: Pinched Morphism Spaces
    • Subsection 5.2.6: Morphism Spaces in the Homotopy Coherent Nerve
  • Section 5.3: Localization
    • Subsection 5.3.1: Localizations of $\infty $-Categories
    • Subsection 5.3.2: Existence of Localizations
    • Subsection 5.3.3: Stability Properties of Localizations
    • Subsection 5.3.4: The Category of Simplices