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Definition df-arw 16448
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 Arrow = (𝑐 ∈ Cat ↦ ran (Homa𝑐))

Detailed syntax breakdown of Definition df-arw
StepHypRef Expression
1 carw 16443 . 2 class Arrow
2 vc . . 3 setvar 𝑐
3 ccat 16096 . . 3 class Cat
42cv 1473 . . . . . 6 class 𝑐
5 choma 16444 . . . . . 6 class Homa
64, 5cfv 5789 . . . . 5 class (Homa𝑐)
76crn 5028 . . . 4 class ran (Homa𝑐)
87cuni 4366 . . 3 class ran (Homa𝑐)
92, 3, 8cmpt 4637 . 2 class (𝑐 ∈ Cat ↦ ran (Homa𝑐))
101, 9wceq 1474 1 wff Arrow = (𝑐 ∈ Cat ↦ ran (Homa𝑐))
Colors of variables: wff setvar class
This definition is referenced by:  arwval  16464  arwrcl  16465
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