In mathematics, and in particular homotopy theory, a hypercovering (or hypercover) is a simplicial object that generalises the Čech nerve of a cover. For the Čech nerve of an open cover U → X {\displaystyle {\mathcal {U}}\to X} , one can show that if the space X {\displaystyle X} is compact and if every intersection of open sets in the cover is contractible, then one can contract these sets and get a simplicial set that is weakly equivalent to X {\displaystyle X} in a natural way.
In mathematics, and in particular homotopy theory, a hypercovering (or hypercover) is a simplicial object that generalises the Čech nerve of a cover. For the Čech nerve of an open cover U → X {\displaystyle {\mathcal {U}}\to X} , one can show that if the space X {\displaystyle X} is compact and if every intersection of open sets in the cover is contractible, then one can contract these sets and get a simplicial set that is weakly equivalent to X {\displaystyle X} in a natural way.
Source: Wikipedia "Hypercovering" · CC BY-SA 4.0
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