Seminář z algebry - 13.2.2020 |
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Další seminář z algebry se koná 13.2.2020 od 13.00 v posluchárně M5. F. Pakhomov
Dilators and Ptykes
Abstrakt: Dilators are endofunctors D:WO->WO preserving pullbacks and directed co-limits, where WO is the category of well-orderings and strictly monotone maps. This notion was introduced by J.-Y. Girard as one of central notions within his approach to certain problems in proof-theory (calculation of proof-theoretic ordinals). Some more sophisticated applications motivate higher-order generalizations of the notion of dilator, known as ptykes. For example, ptykes of the type (WO->WO)->WO are functors from the category of dilators Dil to WO that preserve pullbacks and directed co-limits (here Dil is the category of dilators and Cartesian natural transformations). In the first part of the talk I plan to discuss dilators, some basic results about them, and give some idea about their applications in proof-theory. Next I plan to talk about my approach to the theory of ptykes, where types of ptykes are interpreted as classes of relational structures that are closed under substructures.
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Aktualizováno Čtvrtek, 06 Únor 2020 16:11 |