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 by a smooth map, defined by "integration on the fibres".
- Pushout (category theory): the categorical dual of pullback.
- Pushforward measure: measure induced on the target measure space by a measurable function.
- The transfer operator is the pushforward on the space of measurable functions; its adjoint, the pull-back, is the composition or Koopman operator.
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