The Clowder Project

2.6 The Adjoint Triple $f_{*}\dashv f^{-1}\dashv f_{!}$

• Subsection 2.6.1: Direct Images
  • Definition 2.6.1.1.1: Direct Images
  • Notation 2.6.1.1.2: Further Notation for Direct Images
  • Remark 2.6.1.1.3: Unwinding Definition 2.6.1.1.1
  • Proposition 2.6.1.1.4: Properties of Direct Images I
  • Proposition 2.6.1.1.5: Properties of Direct Images II
• Subsection 2.6.2: Inverse Images
  • Definition 2.6.2.1.1: Inverse Images
  • Remark 2.6.2.1.2: Unwinding Definition 2.6.2.1.1
  • Proposition 2.6.2.1.3: Properties of Inverse Images I
  • Proposition 2.6.2.1.4: Properties of Inverse Images II
• Subsection 2.6.3: Direct Images With Compact Support
  • Definition 2.6.3.1.1: Direct Images With Compact Support
  • Notation 2.6.3.1.2: Further Notation for Direct Images With Compact Support
  • Remark 2.6.3.1.3: Unwinding Definition 2.6.3.1.1
  • Definition 2.6.3.1.4: The Image and Complement Parts of $f_{!}$
  • Example 2.6.3.1.5: Examples of Direct Images With Compact Support
  • Proposition 2.6.3.1.6: Properties of Direct Images With Compact Support I
  • Proposition 2.6.3.1.7: Properties of Direct Images With Compact Support II
• Subsection 2.6.4: A Six-Functor Formalism for Sets
  • Remark 2.6.4.1.1: A Six-Functor Formalism for Sets
  • Proposition 2.6.4.1.2: A Six Functor Formalism for Sets