underlying functor

plural underlying functors

1. category theorya forgetful functor

   1 more example

   3.1.10 Example If you forget [that] you can compose arrows in a category and you forget which arrows are the identities, then you have remembered only that the category is a graph. This gives an underlying functor U#58;#92;mathbf#123;Cat#125;#92;rightarrow#92;mathbf#123;Grf#125;, since every functor is a graph homomorphism although not vice versa.

   1995, Michael Barr with Charles Wells, Category Theory for Computing Science, 2nd edition, University Press, Cambridge, Great Britain: Prentice Hall, §3.1.10, page 57