Definition df-arw 18072

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 (Homa‘𝑐))

Detailed syntax breakdown of Definition df-arw

Step	Hyp	Ref	Expression
1		carw 18067	. 2 class Arrow
2		vc	. . 3 setvar 𝑐
3		ccat 17707	. . 3 class Cat
4	2	cv 1539	. . . . . 6 class 𝑐
5		choma 18068	. . . . . 6 class Homa
6	4, 5	cfv 6561	. . . . 5 class (Homa‘𝑐)
7	6	crn 5686	. . . 4 class ran (Homa‘𝑐)
8	7	cuni 4907	. . 3 class ∪ ran (Homa‘𝑐)
9	2, 3, 8	cmpt 5225	. 2 class (𝑐 ∈ Cat ↦ ∪ ran (Homa‘𝑐))
10	1, 9	wceq 1540	1 wff Arrow = (𝑐 ∈ Cat ↦ ∪ ran (Homa‘𝑐))

This definition is referenced by:  arwval  18088  arwrcl  18089