|zpravodaj ČSKI - prosinec 2017 |
datum: 13.12.2017 v 10:00
název: Brouwerian algebras as negative cones of idempotent involutive residuated lattices
přednášející: Adam Přenosil (UI)
místo konání: UI, 2.patro, místnost č.318
souhrn: In this talk we describe a categorical equivalence between Brouwerian algebras (i.e. Heyting algebras possibly without the lower bound) and a variety of idempotent involutive residuated lattices (InRLs). One direction of this equivalence is given by the negative cone functor, while the opposite direction is given by a certain twist product functor. In particular, it turns out that Brouwerian algebras are precisely the negative cones of idempotent InRLs. This equivalence extends an equivalence between relative Stone algebras (i.e. Godel algebras possibly without the lower bound) and odd Sugihara monoids established by Galatos & Raftery (2012) and recently extended to arbitrary Sugihara monoids by Galatos & Raftery (2015) and Fussner & Galatos (unpublished). We will also sketch how to extend our equivalence in order to cover these cases as well as the case of Abelian l-groups. This talk is based on joint work with Nick Galatos.