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Does anyone know where I can find a description of the opposite category of the category of graphs? The morphisms of the category are graph homomorphisms.

Thank you

  • 13
    What do you have in mind? «The opposite category of the category of graphs» sounds like a great description of the opposite category of the category of graphs to me :-)2012-10-15
  • 1
    What kind of description are you looking for? You just gave a very clear description of it.2012-10-15
  • 0
    I want a category that is equivalent to the dual of the category of graphs. I want the category to be realised, not just an abstract category.2012-10-15
  • 2
    Since the category of graphs is a concrete one (in the technical sense), its opposite ccategory is concrete (because there is a faithful functor $\mathsf{Set}^{\mathrm{op}}\to\mathsf{Set}$, the powerset functor) This gives a realization of sorts...2012-10-15
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    If I'm not mistaken, the category of graphs is a locally finitely presentable category but not a preorder, so its opposite cannot be locally finitely presentable. This means there is no hope of finding a description of it as a category of algebraic structures of some kind.2012-10-15
  • 0
    So it's impossible to find such a thing?2012-10-15
  • 3
    You should make precise what you mean by «such a thing», as otherwise it is impossible to know exactly what you want.2012-10-15
  • 1
    The discussion on p.11 on graph homs and "opposite graphs" in Wolter's "Category Theory and Diagrammatic Reasoning", 2011: http://www.ii.uib.no/~wolter/teaching/v11-inf223/manuscript.pdf may be of interest.2012-11-25
  • 0
    I know this is an old question, but *which* category of graphs? Their are several notions of what a graph morphism is.2013-04-01

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