small category- alternative

Definition 0.1.

A (small) categoryMathworldPlanetmath 𝒞 consists of a set of objects C0 and a set of arrows C1 together with the following structureMathworldPlanetmath:

  • a source map s:C1C0 assigning an object s(f) to each arrow fC1 ,

  • a target map: t:C1C0 assigning an object t(f) to each arrow fC1 ,

  • an identity map 1:C0C1 assigning to each object A an arrow 1A with

  • a composition map :C1×C1C1 assigning to each pair of arrows f,g , such that


    , a third arrow gf with s(gf)=s(f) and t(gf)=t(g).

  • The composition thus defined “” is associative, that is,


    whenever these compositions make sense.

  • the identity map satisfies f1A=f for any f such that s(f)=A and 1Ag=g, and any g such that t(g)=A.


P. A. Zito. 2008. [arXiv: math.CT].* -Categories with non-simple units. ,(Preprint).

Title small category- alternative
Canonical name SmallCategoryAlternative
Date of creation 2013-03-22 18:26:38
Last modified on 2013-03-22 18:26:38
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 14
Author bci1 (20947)
Entry type Definition
Classification msc 22A22
Classification msc 18E05
Classification msc 18-00
Related topic Category
Related topic 2CCategory