PUSHOUT

Pushout

In category theory, a branch of mathematics, a pushout is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain: it is the colimit of the span <math>X \leftarrow Z \rightarrow Y</math>.

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pushout

Noun

  1. Given a pair of morphisms <math>f:Z\rightarrow X</math> and <math>g: Z\rightarrow Y</math> with a common domain, Z, their pushout is a pair of morphisms <math>i_1:X\rightarrow P</math> and <math>i_2:Y\rightarrow P</math> as well as their common codomain, P, such that the equation <math> i_1 \circ f = i_2 \circ g</math> is satisfied, and for which there is the universal property that for any other object Q for which there are also morphisms <math>j_1: X\rightarrow Q</math> and <math>j_2: Y\rightarrow Q</math>; there is a unique morphism <math>u: P\rightarrow Q</math> such that <math> u \circ i_1 = j_1</math> and <math>u \circ i_2 = j_2</math>.


The above text is a snippet from Wiktionary: pushout
and as such is available under the Creative Commons Attribution/Share-Alike License.

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