23/04/2016, 11:45 — 12:15 — Abreu Faro Amphitheatre
Lurdes Sousa, Instituto Politécnico de Viseu, Centro de Matemática da Universidade de Coimbra

From Birkhoff's equational logic to Kan-injectivity logic

In [1] we presented a logic for finitary epimorphisms which can be seen as an extension of Birkhoff's equational logic. In subsequent papers with Jiří Adámek and Michel Hébert, we obtained generalizations in several directions, in particular the Orthogonality Logic ([2,3]). After a first quick account of these results, I will present recent work with Jiří Adámek and Jiří Velebil on a generalization of this last logic in the setting of order-enriched categories.

1. J. Adámek, M. Sobral, L. Sousa, A logic of implications in algebra and coalgebra, Algebra Univers. 61 (2009) 313-337.
2. J. Adámek, M. Hébert, L. Sousa, A logic of orthogonality, Archivum Mathematicum 42, no.4, (2006), 309-334.
3. J. Adámek, M. Hébert, L. Sousa, The orthogonal subcategory problem and the small object argument, Appl. Categ. Structures 17 (2009), no. 3, 211-246.