6 Adjoint Functors

Structure

• 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: Local Objects
  • Subsection 6.2.4: Stability Properties of Reflective Subcategories
  • Subsection 6.2.5: Correspondences
  • Subsection 6.2.6: Local Existence Criterion
  • Subsection 6.2.7: Digression: $\infty $-Categories with Short Morphisms
• 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: Fiberwise Localization
  • Subsection 6.3.5: Universal Localizations
  • Subsection 6.3.6: Subdivision and Localization