# Pre-sheaves of spaces and the Grothendieck construction for infinity-categories

#### by Daniel Stevenson

Abstract: The notion of pre-stack in algebraic geometry can be formulated either in terms of categories fibered in groupoids, or else as a functor to the category of groupoids with composites only preserved up to a coherent system of natural isomorphisms. The device which lets one shift from one perspective to the other is known as the Grothendieck construction’ in category theory.