underlying functor

English

underlying functor (plural underlying functors)

(category theory) a forgetful functor
- 1995, Michael Barr; Charles Wells, Category Theory for Computing Science‎, 2nd edition, University Press, Cambridge, Great Britain: Prentice Hall, §3.1.10, page 57:
  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 ${\\displaystyle U:\\mathbf {Cat} \\rightarrow \\mathbf {Grf} }$ , since every functor is a graph homomorphism although not vice versa.

单词	underlying functor
释义	underlying functor English Noun underlying functor (plural underlying functors) (category theory) a forgetful functor 1995, Michael Barr; Charles Wells, Category Theory for Computing Science‎, 2nd edition, University Press, Cambridge, Great Britain: Prentice Hall, §3.1.10, page 57: 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 ${\\displaystyle U:\\mathbf {Cat} \\rightarrow \\mathbf {Grf} }$ , since every functor is a graph homomorphism although not vice versa.
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