  The main result of this thesis is the construction of a tannakian context
over the category of sup-lattices, associated with an arbitrary Grothendieck
topos, and the attainment of new results in tannakian representation theory
from it.
  Although many results were obtained and published historically linking Galois
and Tannaka theory (see our introduction), these are different and less general
since they assume the existence of Galois closures and work on Galois topos
rather than on arbitrary topos. Instead we, when talking about Galois theory,
mean the extension to arbitrary topos of Joyal and Tierney, critical to get the
results of this thesis.
  The tannakian context associated with a Grothendieck topos is obtained
through the process of taking relations of its localic cover. Then, through an
investigation and exhaustive comparison of the constructions of the Galois and
Tannaka theories, we prove the equivalence of their fundamental recognition
theorems (see section 8).
  Since the (bi)categories of relations of a Grothendieck topos were
characterized by Carboni and Walters, a new recognition-type tannakian theorem
(theorem 8.12) is obtained, essentially different from those known so far.

Category Theory