# pullback

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## English[edit]

### Etymology[edit]

### Noun[edit]

**pullback** (*plural* **pullbacks**)

- The act or result of pulling back; a withdrawal.
- (film) The act of drawing a camera back to broaden the visible scene.
- That which holds back, or causes to recede; a drawback; a hindrance.
- (architecture) The iron hook fixed to a casement to pull it shut, or to hold it partly open at a fixed point.
- (finance) A reduction in the price of a financial instrument after reaching a peak
- (differential geometry) The map between cotangent bundles of manifolds corresponding to a smooth map between smooth manifolds, which at each point is the dual map to the corresponding pushforward.
- (category theory) The limit of a
*corner of arrows*, which is a pair of arrows sharing the same codomain: a Cartesian square or "pullback square". - (category theory) Within a Cartesian square (which has a pair of divergent morphisms and a pair of convergent morphisms) the divergent morphism which is directly opposite to a given one of the convergent morphisms, said to be "along" the convergent morphism which is between that pair of opposite morphisms. (The pullback is said to be "of" the given morphism.)

#### Synonyms[edit]

#### See also[edit]

- (differential geometry) pushforward
- (category theory) pushout

*Part or all of this entry has been imported from the 1913 edition of Webster’s Dictionary, which is now free of copyright and hence in the public domain. The imported definitions may be significantly out of date, and any more recent senses may be completely missing.(See the entry for pullback in *Webster’s Revised Unabridged Dictionary

*, G. & C. Merriam, 1913.)*