Defects in Category Theory: From Functors to Proarrow Equipments

Defects in Category Theory: From Functors to Proarrow Equipments

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24 of 25

24 of 25

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Defects in Category Theory: From Functors to Proarrow Equipments

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  1. 1 Intro
  2. 2 The defect of a covariant f.p. functor
  3. 3 The defect of a contravariant f.p. functor
  4. 4 The defect of a covariant additive functor
  5. 5 The defect of a contravariant additive functor
  6. 6 Questions
  7. 7 Outline of the results
  8. 8 Conventions
  9. 9 Main tools
  10. 10 Definition of profunctor
  11. 11 Examples of profunctors
  12. 12 Composition of profunctors
  13. 13 Triangle of profunctors
  14. 14 Bitensored category
  15. 15 The Yoneda and coYoneda lemmas
  16. 16 Defects of a profunctor
  17. 17 Adjunctions for defects
  18. 18 The contravariant defect of a f.p. functor (revisited)
  19. 19 The contravariant defect of an additive functor (revisited)
  20. 20 The covariant defect of an additive functor (revisited)
  21. 21 Isbell duality interchanges representable functors
  22. 22 Isbell duals for profunctors
  23. 23 Isbell duals factor through defects
  24. 24 Equipment
  25. 25 Defects are adjoint to Yoneda embeddings

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