8 The Yoneda Embedding

Structure

• Section 8.1: Twisted Arrows and Cospans
  • Subsection 8.1.1: The Twisted Arrow Construction
  • Subsection 8.1.2: Homotopy Transport for Twisted Arrows
  • Subsection 8.1.3: The Universal Property of Twisted Arrows
  • Subsection 8.1.4: The Cospan Construction
  • Subsection 8.1.5: Morphisms in the Duskin Nerve
  • Subsection 8.1.6: Cospans in $\infty $-Categories
  • Subsection 8.1.7: Thin $2$-Simplices of $\operatorname{Cospan}(\operatorname{\mathcal{C}})$
• Section 8.2: The Yoneda Embedding
  • Subsection 8.2.1: Yoneda's Lemma
  • Subsection 8.2.2: Profunctors of $\infty $-Categories
  • Subsection 8.2.3: Hom-Functors for $\infty $-Categories
  • Subsection 8.2.4: Strict Models for Hom-Functors
  • Subsection 8.2.5: The Yoneda Embedding
  • Subsection 8.2.6: Representable Profunctors
  • Subsection 8.2.7: Adjunctions as Profunctors