PlanetPhysics/Small Category

A (small) category consists of a set of objects and a set of arrows together with the following structure:

  • a source map assigning an object to each arrow ,
  • a target map: assigning an object t(f) to each arrow ,
  • an identity map assigning to each object an arrow with
  • a composition map assigning to each pair of arrows , such that , a third arrow with and .
  • The composition thus defined "" is associative, that is, whenever these compositions make sense.
  • the identity map satisfies for any such that and , and any such that .

References

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