  The purpose of this work is twofold: to expose the existing similarities
between the generalizations of the Tannaka and Galois theories, and on the
other hand, to develop in detail our own treatment of part of the content of
Joyal and Street [1] paper, generalizing from vector spaces to an abstract
tensor category. We also develop in detail the proof of the Tannaka equivalence
of categories in the case of vector spaces. Saavedra Rivano [2], Deligne and
Milne [3] generalize classical Tannaka theory to the context of K-linear tensor
(or monoidal) categories. They obtain a lifting-equivalence into a category of
\group representations" for a finite-dimensional vector space valued monoidal
functor. This lifting theorem is similar to the one of Grothendieck Galois
theory [4] for a finite sets valued functor. On the other hand, Joyal and
Street [1] work on the algebraic side of the duality between algebra and
geometry, and also obtain a lifting-equivalence, but now to the category of
finite-dimensional comodules over a Hopf algebra. In this work we follow the
ideas of Joyal and Street and prove their lifting-equivalence, and then we show
how it corresponds, by dualizing, to the ones of Saavedra Rivano [2] and
Deligne and Milne [3]. Text is in spanish, but a brief english introduction is
provided.
