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Commutative diagram of a pullback in category theory.


pull +‎ back


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.


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 The imported definitions may be significantly out of date, and any more recent senses may be completely missing.