2 Higher Category Theory

Structure

• Chapter 6: Adjoint Functors
  • Section 6.1: Adjunctions in $2$-Categories
    • Subsection 6.1.1: Adjunctions
    • Subsection 6.1.2: Adjuncts
    • Subsection 6.1.3: Uniqueness of Adjoints
    • Subsection 6.1.4: Adjoints of Isomorphisms
    • Subsection 6.1.5: Composition of Adjunctions
    • Subsection 6.1.6: Duality in Monoidal Categories
  • Section 6.2: Adjoint Functors Between $\infty $-Categories
    • Subsection 6.2.1: Adjunctions of $\infty $-Categories
    • Subsection 6.2.2: Reflective Subcategories
    • Subsection 6.2.3: Correspondences
    • Subsection 6.2.4: Existence of Adjoints
  • Section 6.3: Localization
    • Subsection 6.3.1: Localizations of $\infty $-Categories
    • Subsection 6.3.2: Existence of Localizations
    • Subsection 6.3.3: Reflective Localizations
    • Subsection 6.3.4: Stability Properties of Localizations
    • Subsection 6.3.5: Fiberwise Localization
    • Subsection 6.3.6: Universal Localizations
    • Subsection 6.3.7: Subdivision and Localization
• Chapter 7: Limits and Colimits
  • Section 7.1: Limits and Colimits
    • Subsection 7.1.1: Initial and Final Objects of $\infty $-Categories
    • Subsection 7.1.2: Representable Fibrations
    • Subsection 7.1.3: Limits and Colimits
    • Subsection 7.1.4: Preservation of Limits and Colimits
    • Subsection 7.1.5: Relative Limits and Colimits
  • Section 7.2: Cofinality
    • Subsection 7.2.1: Cofinal Morphisms of Simplicial Sets
    • Subsection 7.2.2: Cofinality and Limits
    • Subsection 7.2.3: Quillen's Theorem A for $\infty $-Categories
    • Subsection 7.2.4: Filtered $\infty $-Categories
    • Subsection 7.2.5: Local Characterization of Filtered $\infty $-Categories
    • Subsection 7.2.6: Left Fibrations over Filtered $\infty $-Categories
    • Subsection 7.2.7: Cofinal Approximation
    • Subsection 7.2.8: Sifted Simplicial Sets