# pullback

## English

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Commutative diagram of a pullback in category theory.

pull +‎ back

### Noun

pullback (plural pullbacks)

1. The act or result of pulling back; a withdrawal.
2. (film) The act of drawing a camera back to broaden the visible scene.
3. That which holds back, or causes to recede; a drawback; a hindrance.
4. (architecture) The iron hook fixed to a casement to pull it shut, or to hold it partly open at a fixed point.
5. (finance) A reduction in the price of a financial instrument after reaching a peak
6. (category theory) Given a pair of morphisms $f:X\rightarrow Z$ and $g: Y\rightarrow Z$ with a common codomain, Z, their pullback is a pair of morphisms $p_1:P\rightarrow X$ and $p_2:P\rightarrow Y$ as well as their common domain, P, such that the equation $f\circ p_1 = g\circ p_2$ is satisfied, and for which there is the universal property that for any other object Q for which there are also morphisms $q_1: Q\rightarrow X$, $q_2: Q\rightarrow Y$; there is a unique morphism $u: Q\rightarrow P$ such that $p_1\circ u = q_1$ and $p_2 \circ u = q_2$.

#### Antonyms

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 The imported definitions may be significantly out of date, and any more recent senses may be completely missing.