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Mirrors > Home > MPE Home > Th. List > df-epi | Structured version Visualization version GIF version |
Description: Function returning the epimorphisms of the category 𝑐. JFM CAT1 def. 11. (Contributed by FL, 8-Aug-2008.) (Revised by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
df-epi | ⊢ Epi = (𝑐 ∈ Cat ↦ tpos (Mono‘(oppCat‘𝑐))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cepi 17234 | . 2 class Epi | |
2 | vc | . . 3 setvar 𝑐 | |
3 | ccat 17167 | . . 3 class Cat | |
4 | 2 | cv 1542 | . . . . . 6 class 𝑐 |
5 | coppc 17214 | . . . . . 6 class oppCat | |
6 | 4, 5 | cfv 6380 | . . . . 5 class (oppCat‘𝑐) |
7 | cmon 17233 | . . . . 5 class Mono | |
8 | 6, 7 | cfv 6380 | . . . 4 class (Mono‘(oppCat‘𝑐)) |
9 | 8 | ctpos 7967 | . . 3 class tpos (Mono‘(oppCat‘𝑐)) |
10 | 2, 3, 9 | cmpt 5135 | . 2 class (𝑐 ∈ Cat ↦ tpos (Mono‘(oppCat‘𝑐))) |
11 | 1, 10 | wceq 1543 | 1 wff Epi = (𝑐 ∈ Cat ↦ tpos (Mono‘(oppCat‘𝑐))) |
Colors of variables: wff setvar class |
This definition is referenced by: oppcmon 17243 |
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