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Definiton of a category question

  1. Nov 15, 2003 #1
    "for each object A there is an arrow id_A called the identity of A whose source and target are both A."

    wouldnt this definition imply that id_A is a point instead of an arrow?
    if not help me visualise this.

    btw this should be the notation id_A:A->A
     
  2. jcsd
  3. Nov 15, 2003 #2

    HallsofIvy

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    Categories contain objects and "arrows" (I would call them "relations") but I've never heard of a "point" being defined for a general category.

    You may be thinking of the object as a single "point" and then identifying the arrow (from the object to itself) with that "point".

    Remember that in general, given two objects in a category, there may be many arrows from one to another so you cannot identify arrows with objects. In particular, there may be many arrows from a given category to itself. The arrow "id_A" is a specific one of those so you certainly cannot identify "id_A" with the object.
     
  4. Nov 16, 2003 #3
    i wouldn't call them relations because a relation is generally used in reference to being some subset of the cartesian product of sets. arrows are not sets in general.
     
  5. Nov 16, 2003 #4

    selfAdjoint

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    Objects and morphism is the usual terminology. If it helps, you can think of morphisms as arrows and objects as boxes, as in a flow chart.
     
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