• Corpus ID: 235790470

Relative topos theory via stacks

  title={Relative topos theory via stacks},
  author={Olivia Caramello and Riccardo Zanfa},
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of ${\mathcal{C}}$-indexed categories. This represents a wide generalization of the classical adjunction between presheaves on a topological space and bundles over it, and allows one to interpret several constructions on sheaves and stacks in a geometrical way; in…