Seminario / Clementino
Martedi' 23 maggio 2017, alle ore 14.30, in Sala Rappresentanza,
la Prof.ssa Maria Manuel Clementino, Center for Mathematics, University of Coimbra
terra' un seminario dal titolo:
"Simple reflections revisited"
We present a notion of simple monad that generalises the notion of simple reflection of Cassidy-H ebert-Kelly  to order-enriched categories, and study the factorisations they induce.
These factorisations are lax orthogonal, as defined in , and, as for the classical case of , can be characterised by a cancellation property.
We will show that filter monads on topological T0-spaces are simple, and show that the factorisations they induced, studied in , are lax orthogonal.
(Joint work with Ignacio L ópez Franco, [3,4].)
 C. Cassidy, M. H ébert, G.M. Kelly, Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc. (Series A) 38 (1985) 287-329.
 F. Cagliari, M.M. Clementino, S. Mantovani, Fibrewise injectivity and Kock-Z"oberlein monads, J. Pure Appl. Algebra 216 (2012) 2411-2424.
 M.M. Clementino, I. L ópez Franco, Lax orthogonal factorisation systems, Adv. Math. 302 (2016) 458-528.
 M.M. Clementino, I. L ópez Franco, Lax orthogonal factorisations in ordered structures, DMUC Preprint 17-06, University of Coimbra; arXiv 1702.02602.