A Quick and Simple Dictionary

pullback

1. Noun.  The act or result of pulling back; a withdrawal.
2. Noun.  That which holds back, or causes to recede; a drawback; a hindrance.
3. Noun.  (architecture) The iron hook fixed to a casement to pull it shut, or to hold it partly open at a fixed point.
4. Noun.  (finance) A reduction in the price of a financial instrument after reaching a peak.
5. Noun.  (category theory) Given a pair of arrows $f:Y\; ightarrow\; X$ and $g:\; Z\; ightarrow\; X$ with a common codomain, ''X'', their '''pullback''' is a pair of arrows $u:P\; ightarrow\; Y$ and $v:P\; ightarrow\; Z$ with common domain, ''P'', such that the equation $fcirc\; u\; =\; gcirc\; v$ is satisfied, and for which there is the ''universal property'' that for any other object ''W'' for which there are also arrows $m:\; W\; ightarrow\; Y$, $n:\; W\; ightarrow\; Z$; there is a unique arrow $k:\; W\; ightarrow\; P$ such that $ucirc\; k\; =\; m$ and $vcirc\; k\; =\; n$.