Pushforward

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The notion of pushforward in mathematics is "dual" to the notion of pullback, and can mean a number of different, but closely related things.

• Pushforward (differential): the differential of a smooth map between manifolds, and the "pushforward" operations it defines.
• Direct image sheaf: the pushforward of a sheaf by a map.
• Pushforward (homology): the map induced in homology by a continuous map between topological spaces.
• Fiberwise integral: the direct image of a differential form or cohomology class by a smooth map, defined by "integration on the fibres".
• Pushout (category theory): the categorical dual of Pullback (category theory).
• Pushforward measure: the measure induced on the target measure space by a measurable function.

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