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Canonical extensions of lattices are more than perfect
Title Canonical extensions of lattices are more than perfect Author info Andrew P. K. Craig, Maria J. Gouveia, Miroslav Haviar Author Craig Andrew, P. K. (34%)
Co-authors Gouveia Maria Joao (33%)
Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Source document Algebra Universalis. Vol. 83, no. 2 (2022), pp. [1-17]. - Basel : Springer Nature Switzerland AG, 2022 Keywords kanonické rozšírenia matematika - mathematics Form. Descr. články - journal articles Language English Country Switzerland Annotation In a paper published in 2015, we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical exten sions of lattices. Here, we firstly introduce morphisms of TiRS structures and put our correspondence between TiRS graphs and TiRS frames into a full categorical framework. We then answer Problem 2 from our 2015 paper by characterising the perfect lattices that are dual to TiRS frames (and hence TiRS graphs). We introduce a new subclass of perfect lattices called PTi lattices and show that the canonical extensions of lattices are PTi lattices, and so are ‘more’ than just perfect lattices. We illustrate the correspondences between classes of our newly-described PTi lattices and classes of TiRS graphs by examples. We conclude by outlining a direction for future research. URL Link na plný text Public work category ADC No. of Archival Copy 51538 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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