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Definition df-arw 14145
Description: Definition of the set of arrows of a category. We will use the term "arrow" to denote a morphism tagged with its domain and codomain, as opposed to  Hom, which allows hom-sets for distinct objects to overlap. (Contributed by Mario Carneiro, 11-Jan-2017.)
Assertion
Ref Expression
df-arw  |- Nat  =  ( c  e.  Cat  |->  U.
ran  (Homa
`  c ) )

Detailed syntax breakdown of Definition df-arw
StepHypRef Expression
1 carw 14140 . 2  class Nat
2 vc . . 3  set  c
3 ccat 13852 . . 3  class  Cat
42cv 1648 . . . . . 6  class  c
5 choma 14141 . . . . . 6  class Homa
64, 5cfv 5421 . . . . 5  class  (Homa `  c
)
76crn 4846 . . . 4  class  ran  (Homa `  c
)
87cuni 3983 . . 3  class  U. ran  (Homa `  c )
92, 3, 8cmpt 4234 . 2  class  ( c  e.  Cat  |->  U. ran  (Homa `  c ) )
101, 9wceq 1649 1  wff Nat  =  ( c  e.  Cat  |->  U.
ran  (Homa
`  c ) )
Colors of variables: wff set class
This definition is referenced by:  arwval  14161  arwrcl  14162
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