Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-arw | Structured version Visualization version Unicode 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 , which allows hom-sets for distinct objects to overlap. (Contributed by Mario Carneiro, 11-Jan-2017.) |
Ref | Expression |
---|---|
df-arw | Nat Homa |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | carw 16672 | . 2 Nat | |
2 | vc | . . 3 | |
3 | ccat 16325 | . . 3 | |
4 | 2 | cv 1482 | . . . . . 6 |
5 | choma 16673 | . . . . . 6 Homa | |
6 | 4, 5 | cfv 5888 | . . . . 5 Homa |
7 | 6 | crn 5115 | . . . 4 Homa |
8 | 7 | cuni 4436 | . . 3 Homa |
9 | 2, 3, 8 | cmpt 4729 | . 2 Homa |
10 | 1, 9 | wceq 1483 | 1 Nat Homa |
Colors of variables: wff setvar class |
This definition is referenced by: arwval 16693 arwrcl 16694 |
Copyright terms: Public domain | W3C validator |