localization

local object, local morphism

reflective localization

Bousfield localization, simplicial localization

descent

cover

descent object, descent morphism

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

cohomological descent

monadic descent, higher monadic descent

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A localization is called reflective if the full subcategory of local objects is a reflective subcategory/reflective sub-(∞,1)-category.