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On Finitary Functors and Their Presentation

On Finitary Functors and Their Presentation. Jiří Adámek , Stefan Milius and Larry Moss. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A. Why finitary functors are interesting. (J. Adámek 1974). (J. Worrell 1999).

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On Finitary Functors and Their Presentation

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  1. On FinitaryFunctorsandTheirPresentation JiříAdámek, Stefan Miliusand Larry Moss TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A

  2. Whyfinitaryfunctorsareinteresting (J. Adámek 1974) (J. Worrell 1999) (J. Adámek & V. Trnková 1990) Ourresults. Applicationof G.M. Kelly & A.J. Power 1993 Relatedto: Bonsangue & Kurz (2006); Kurz & Rosicky (2006); Kurz & Velebil (2011) Strengtheningof: van Breugel, Hermida, Makkai, Worrell (2007)

  3. Locallyfinitelypresentable (lfp) categories „Definition.“ Examples.

  4. Example: presentationofthe finite power-set functor

  5. From Set tolfpcategories Following Kelly & Power (1993) Construction

  6. Example in posets

  7. Finitaryfunctorsandpresentations Theorem. Proof. Theorem.

  8. The Hausdorfffunctor Non-determinismforsystemswithcompletemetricstatespace.

  9. AccessabilityoftheHausdorfffunctor Theorem. van Breugel, Hermida, Makkai, Worrell (2007) Makkai & Pare (1989) commutative idempotent associative

  10. Yes, wecan! preservescolimits Proposition. Bad news. But:

  11. FinitarynessoftheHausdorfffunctor Theorem. Proof.

  12. PresentationoftheHausdorfffunctor separablespaces = countablypresentable locallycountablypresentable Proposition. Proof.

  13. Conclusionsandfuturework • Finitaryfunctors on lfpcategoriesarepreciselythosehaving a finitarypresentation • The Hausdorfffunctorisfinitaryandhas a presentationbyoperationswith finite arity • Future work • Kantorovich functor on CMS (formodellingprobabilistic non-determinism) • Relation ofourpresentationsto rank-1 presentationsas in Bonsangue & Kurz

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