Page 11 - Textos de Matemática Vol. 46

MATHEMATICAL GREETINGS TO MANUELA SOBRAL
GEORGE JANELIDZE
Following the talk given at the Workshop on Categorical Methods in Algebra and Topology in Honour of Manuela Sobral on the occasion of her 70th birthday
(Coimbra, 24-26 January 2014)
The Coimbra Workshop was devoted to category theory, but first of all it was devoted to our admiration of Professor Maria Manuela Oliveira de Sousa Antunes Sobral, a mathematician who introduced category theory in her coun- try.
Thanks to beautiful speeches by Eduardo Marques de S´a at the Opening and by Walter Tholen at the Conference Dinner, I could indeed reduce my talk to purely mathematical greetings, presented now in the written form as follows:
It is good to begin with the moment when Manuela decided to do her PhD in mathematics (as we say these days). For family reasons this was happening in Southern Africa, and particularly in South Africa, which was scientifically most advanced in that part of the World. The suggestion for research Manuela got was to study either category theory or homological algebra, which was very nice... I wish I could give such a suggestion to my PhD students... No surprise that Manuela chose category theory, but what happened next is a miracle, which I shall now try to describe in a few sentences:
As we all know, in contrast to set-theoretic mathematics being split into many branches corresponding to many important types of mathematical struc- tures, the purpose of category theory is to unify. Therefore general-categorical constructions and results are supposed to be equally applicable to, say, alge- braic and topological structures, and not to be merely generalized copies of what is done for any single type of structure, even if that type of structure is a very important one. In particular, many years ago some developments in categorical topology were heavily criticized for creating categorical terminol- ogy suitable only for topological and closely related structures. But imagine a PhD student, who only begins to study category theory in an environment where categorical topology clearly dominates. Can we expect such a student to understand, in spite of the fact that categorical topology is so abstract and
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