nLab descent and locality - contents

localization

• local object, local morphism

• reflective localization

  • category of sheaves, (∞,1)-category of (∞,1)-sheaves

• Bousfield localization, simplicial localization

descent

• cover

• descent object, descent morphism

  • matching family

• sheaf, (2,1)-sheaf/stack, 2-sheaf,(∞,1)-sheaf/∞-stack

• cohomological descent

• monadic descent, higher monadic descent

  • Sweedler coring, descent in noncommutative algebraic geometry

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