The University of Manchester Category Theory Group

Descent Theory

Raffael Stenzel

Descent is a categorical abstraction of the local to global principle as known from topology and geometry. Its origins go back to Grothendieck's development of algebraic geometry in schematic terms. We define descent as a property of suitably typed functors in considerable generality, discuss various examples and incarnations thereof that arise in the (higher) categorical literature, and speak about its centralĀ  role in (higher) topos theory.

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