2.4 Powersets

  • Subsection 2.4.1: Characteristic Functions
    • Definition 2.4.1.1.1: Characteristic Functions
    • Remark 2.4.1.1.2: Characteristic Functions as Decategorifications of Presheaves
    • Proposition 2.4.1.1.3: Properties of Characteristic Functions
  • Subsection 2.4.2: The Yoneda Lemma for Sets
    • Proposition 2.4.2.1.1: The Yoneda Lemma for Sets
    • Corollary 2.4.2.1.2: The Characteristic Embedding Is Fully Faithful
  • Subsection 2.4.3: Powersets
    • Definition 2.4.3.1.1: Powersets
    • Remark 2.4.3.1.2: Powersets as Decategorifications of Co/Presheaf Categories
    • Proposition 2.4.3.1.3: Properties of Powersets: As Categories
    • Proposition 2.4.3.1.4: Properties of Powersets: Functoriality and Adjointness
    • Proposition 2.4.3.1.5: Properties of Powersets: Monoidality
    • Proposition 2.4.3.1.6: Properties of Powersets: As Sets of Functions/Relations
    • Remark 2.4.3.1.7: Powersets as Sets of Functions and Un/Straightening
    • Proposition 2.4.3.1.8: Properties of Powersets: As Free Cocompletions
  • Subsection 2.4.4: Direct Images
  • Subsection 2.4.5: Inverse Images
  • Subsection 2.4.6: Direct Images With Compact Support
    • Definition 2.4.6.1.1: Direct Images With Compact Support
    • Notation 2.4.6.1.2: Further Notation for Direct Images With Compact Support
    • Remark 2.4.6.1.3: Unwinding Definition 2.4.6.1.1
    • Definition 2.4.6.1.4: The Image and Complement Parts of $f_{!}$
    • Example 2.4.6.1.5: Examples of Direct Images With Compact Support
    • Proposition 2.4.6.1.6: Properties of Direct Images With Compact Support I
    • Proposition 2.4.6.1.7: Properties of Direct Images With Compact Support II
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