MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-arw Structured version   Unicode version

Definition df-arw 15630
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 15625 . 2  class Nat
2 vc . . 3  setvar  c
3 ccat 15278 . . 3  class  Cat
42cv 1404 . . . . . 6  class  c
5 choma 15626 . . . . . 6  class Homa
64, 5cfv 5569 . . . . 5  class  (Homa `  c
)
76crn 4824 . . . 4  class  ran  (Homa `  c
)
87cuni 4191 . . 3  class  U. ran  (Homa `  c )
92, 3, 8cmpt 4453 . 2  class  ( c  e.  Cat  |->  U. ran  (Homa `  c ) )
101, 9wceq 1405 1  wff Nat  =  ( c  e.  Cat  |->  U.
ran  (Homa
`  c ) )
Colors of variables: wff setvar class
This definition is referenced by:  arwval  15646  arwrcl  15647
  Copyright terms: Public domain W3C validator