Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Graph and Free Graph in Category Theory

  1. Oct 16, 2008 #1
    Cat(FG, B) [tex]\cong[/tex]Grph(G, UB)

    Cat denotes the category of all small categories and Grph denotes the category of all small graphs.
    G is a small graph which consists of small set O of objects and small set A of arrows f (CWM, PP48-51)
    UB is a forgetful functor applied to category B which is an underlying graph of a category B.
    Morphism of graphs D:G->UB corresponds to D[tex]\acute{}[/tex]:FG->B

    I can't figure out how D[tex]\acute{}[/tex] looks like and how the mapping behaves.
    For D:G->UB, CWM (p50) says it sends each arrow f:a1->a2 of the given graph G to the string <a1,f,a2> of length 2 in UB.

    Now, if G is freely generated to make a category FG, how is it generated and how does it look like?
    A category itself can be described in a graph form. What would be the difference between B and UB if a forgetful functor is applied to B?

    Any advice will be appreciated.
     
    Last edited: Oct 16, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Graph and Free Graph in Category Theory
  1. Graph theory (Replies: 10)

  2. Graph Theory (Replies: 3)

  3. Graph Theory (Replies: 1)

Loading...