Platzhalter fr Bild Bild auf Titelfolie hinter das
Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen On Finitary Functors and Their Presentation Jiří Adámek, Stefan Milius and Larry Moss
Why finitary functors are interesting (J. Adámek 1974) (J. Worrell 1999) (J. Adámek & V. Trnková 1990) Our results. Application of G. M. Kelly & A. J. Power 1993 Related to: Bonsangue & Kurz (2006); Kurz & Rosicky (2006); Kurz & Velebil (2011) Strengthening of: van Breugel, Hermida, Makkai, Worrell (2007) CMCS 2012 | Stefan Milius | April 1, 2012 | S. 2
Locally finitely presentable (lfp) categories „Definition. “ Examples. CMCS 2012 | Stefan Milius | April 1, 2012 | S. 3
Example: presentation of the finite power-set functor CMCS 2012 | Stefan Milius | April 1, 2012 | S. 5
From Set to lfp categories Following Kelly & Power (1993) Construction CMCS 2012 | Stefan Milius | April 1, 2012 | S. 6
Example in posets CMCS 2012 | Stefan Milius | April 1, 2012 | S. 7
Finitary functors and presentations Theorem. Proof. Theorem. CMCS 2012 | Stefan Milius | April 1, 2012 | S. 8
The Hausdorff functor Non-determinism for systems with complete metric state space. CMCS 2012 | Stefan Milius | April 1, 2012 | S. 9
Accessability of the Hausdorff functor van Breugel, Hermida, Makkai, Worrell (2007) Theorem. Makkai & Pare (1989) associative commutative idempotent CMCS 2012 | Stefan Milius | April 1, 2012 | S. 10
Yes, we can! preserves colimits Proposition. Bad news. But: CMCS 2012 | Stefan Milius | April 1, 2012 | S. 11
Finitaryness of the Hausdorff functor Theorem. Proof. CMCS 2012 | Stefan Milius | April 1, 2012 | S. 12
Presentation of the Hausdorff functor separable spaces = countably presentable locally countably presentable Proposition. Proof. CMCS 2012 | Stefan Milius | April 1, 2012 | S. 13
Conclusions and future work Finitary functors on lfp categories are precisely those having a finitary presentation The Hausdorff functor is finitary and has a presentation by operations with finite arity Future work Kantorovich functor on CMS (for modelling probabilistic non-determinism) Relation of our presentations to rank-1 presentations as in Bonsangue & Kurz CMCS 2012 | Stefan Milius | April 1, 2012 | S. 14
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