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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 [1] to order-enriched categories, and study the factorisations they induce.
These factorisations are lax orthogonal, as defined in [3], and, as for the classical case of [1], 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 [2], are lax orthogonal.
(Joint work with Ignacio L ópez Franco,  [3,4].)

[1] C. Cassidy, M. H ébert, G.M. Kelly, Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc. (Series A) 38 (1985) 287-329.
[2] F. Cagliari, M.M. Clementino, S. Mantovani, Fibrewise injectivity and Kock-Z"oberlein monads, J. Pure Appl. Algebra 216 (2012) 2411-2424.
[3] M.M. Clementino, I. L ópez Franco, Lax orthogonal factorisation systems, Adv. Math. 302 (2016) 458-528.
[4] M.M. Clementino, I. L ópez Franco, Lax orthogonal factorisations in ordered structures, DMUC Preprint 17-06, University of Coimbra; arXiv 1702.02602.

16 maggio 2017
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