"underlying functor" meaning in All languages combined

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          "ref": "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:",
          "text": "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#x3A;#x5C;mathbf#x7B;Cat#x7D;#x5C;rightarrow#x5C;mathbf#x7B;Grf#x7D;, since every functor is a graph homomorphism although not vice versa.",
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          "text": "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#x3A;#x5C;mathbf#x7B;Cat#x7D;#x5C;rightarrow#x5C;mathbf#x7B;Grf#x7D;, since every functor is a graph homomorphism although not vice versa.",
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