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Mirrors > Home > MPE Home > Th. List > df-arw | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-arw | ⊢ Arrow = (𝑐 ∈ Cat ↦ ∪ ran (Homa‘𝑐)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | carw 17528 | . 2 class Arrow | |
2 | vc | . . 3 setvar 𝑐 | |
3 | ccat 17167 | . . 3 class Cat | |
4 | 2 | cv 1542 | . . . . . 6 class 𝑐 |
5 | choma 17529 | . . . . . 6 class Homa | |
6 | 4, 5 | cfv 6380 | . . . . 5 class (Homa‘𝑐) |
7 | 6 | crn 5552 | . . . 4 class ran (Homa‘𝑐) |
8 | 7 | cuni 4819 | . . 3 class ∪ ran (Homa‘𝑐) |
9 | 2, 3, 8 | cmpt 5135 | . 2 class (𝑐 ∈ Cat ↦ ∪ ran (Homa‘𝑐)) |
10 | 1, 9 | wceq 1543 | 1 wff Arrow = (𝑐 ∈ Cat ↦ ∪ ran (Homa‘𝑐)) |
Colors of variables: wff setvar class |
This definition is referenced by: arwval 17549 arwrcl 17550 |
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