Categories in Algebra and Topology


Part I: Introduction to Category Theory:
Categories, functors and natural transformations. Isomorphism and equivalence of categories. Construction of new categories: subcategories, product of categories and dual category. Categorical duality principle. Limits and colimits. Functor categories. Representable functors. Yoneda Lemma and Yoneda embedding. Adjoints and limits. Existence of adjoints (Freyd's Theorem).

Part II: It includes topics from the list below, chosen according to the interests of the students:
Monads and categories of Eilenberg-Moore algebras. Cartesian closed categories. Toposes. Locales. Exact and regular categories. Additive, abelian, semi-abelian categories and homological categories.

Research and Events


  • PhD Defense
    Fernando Lucatelli Nunes - Pseudomonads and Descent
    10:00 - Sala dos Capelos, Univ. Coimbra
    January 24, 2018
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Defended Theses

  • Descent theory of (T,V)-categories: global-descent and étale-descent
      Pier Giorgio Basile (September 2017)
      Maria Manuel Clementino
  • Representations of generalized quivers
      Artur Duarte Ferreira de Araújo (June 2017)
      Peter Gothen
  • On semisimple Hopf actions
      Deividi Ricardo Pansera (June 2017)
      Christian Edgar Lomp
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