The Clowder Project

8.7 The Adjoint Pairs $R_{!}\dashv R_{-1}$ and $R^{-1}\dashv R_{*}$

• Subsection 8.7.1: Direct Images
  • Definition 8.7.1.1.1: Direct Images
  • Warning 8.7.1.1.2: Notation for Direct Images Is Confusing
  • Remark 8.7.1.1.3: Unwinding Definition 8.7.1.1.1
  • Proposition 8.7.1.1.4: Properties of Direct Images I
  • Proposition 8.7.1.1.5: Properties of Direct Images II
• Subsection 8.7.2: Coinverse Images
  • Definition 8.7.2.1.1: Coinverse Images
  • Remark 8.7.2.1.2: Unwinding Definition 8.7.2.1.1
  • Definition 8.7.2.1.3: The Domain and Complement Parts of $R_{-1}$
  • Proposition 8.7.2.1.4: Properties of Coinverse Images I
  • Proposition 8.7.2.1.5: Properties of Coinverse Images II
• Subsection 8.7.3: Inverse Images
  • Definition 8.7.3.1.1: Inverse Images
  • Remark 8.7.3.1.2: Unwinding Definition 8.7.3.1.1
  • Proposition 8.7.3.1.3: Properties of Inverse Images I
  • Proposition 8.7.3.1.4: Properties of Inverse Images II
• Subsection 8.7.4: Codirect Images
  • Definition 8.7.4.1.1: Codirect Images
  • Remark 8.7.4.1.2: Unwinding Definition 8.7.4.1.1
  • Definition 8.7.4.1.3: The Image and Complement Parts of $R_{*}$
  • Proposition 8.7.4.1.4: Properties of Codirect Images I
  • Proposition 8.7.4.1.5: Properties of Codirect Images II
• Subsection 8.7.5: A Six-Functor Formalism for Sets, Part II
  • Explanation 8.7.5.1.1: A Six-Functor Formalism for Sets II
  • Proposition 8.7.5.1.2: A Six-Functor Formalism for Sets II
• Subsection 8.7.6: Functoriality of Powersets
  • Proposition 8.7.6.1.1: Functoriality of Powersets I
• Subsection 8.7.7: Functoriality of Powersets: Relations on Powersets
  • Definition 8.7.7.1.1: The Relation on Powersets Associated to a Relation
  • Remark 8.7.7.1.2: Unwinding Definition 8.7.7.1.1
  • Proposition 8.7.7.1.3: Functoriality of Powersets II