Page 13 - Textos de Matemática Vol. 46

MATHEMATICAL GREETINGS TO MANUELA SOBRAL 3
(I) Grothendieck descent theory: the papers devoted to it are [11]-[14], [16], [17], [19]-[21], [23], [24], [27], [31]. Many of these papers were written jointly either with W. Tholen or with me, and one of them (a survey paper) with both of us.
(II) The paper [15] with J. Ad´amek, R. El Bashir, and J. Velebil characterizes lax epimorphisms in Cat.
(III) The paper [18] with J. MacDonald is a survey on monads, which, to- gether with the survey paper [19] (on descent), are chapters in the book “Categorical Foundations” (Cambridge, 2004).
(IV) The papers [22] and [26] with J. Ad´amek and L. Sousa are devoted to categorical-algebraic logic.
(V) Our paper [25] was inspired by one of our attempts (unsuccessful so far) to characterize effective (co)descent morphisms of distributive lattices via the so-called Priestley spaces.
(VI) The papers [28], [29], [30], [32], all with N. Martins-Ferreira, the last three of them, involving monoids, also with A. Montoli, and the last two also with D. Bourn, are devoted to categorical semidirect products.
In fact the theory of monads plays a significant role in almost all of these papers, as well as in Manuela’s earlier work.
Not saying more about Manuela’s recent work, I cannot, however, resist mentioning one of her first contributions to descent theory:
It is well known that the effective descent morphisms in the category Top of topological spaces were fully characterized by J. Reiterman and W. Tholen in terms of ultrafilter convergence. Before having this remarkable result it was not even known whether every descent morphism in Top is an effective descent morphism, and the Reiterman-Tholen counter-example gave the impression that understanding this problem requires entering the somewhat elusive world of ultrafilters. But Manuela’s counter-example was finite – actually it was a map from a six-element space to a three-element space – showing that life is much easier than expected, and initiating various further developments.
Another miracle of Manuela is her way of building her school of category theory at Coimbra. Unless every Portuguese student is a genius, I cannot imag- ine how one professor could get three students as brilliant as Maria Manuel, Lurdes, and Jorge at the same university. And then Manuela, instead of teach- ing these students alone, which she was perfectly capable of doing, finds three brilliant co-supervisors, respectively: Walter Tholen, Jiˇr´ı Ad´amek, and Bern- hard Banaschewski – and Maria Manuel becomes one of the best students of