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Mirrors > Home > MPE Home > Th. List > df-iso | Structured version Visualization version GIF version |
Description: Function returning the isomorphisms of the category 𝑐. Definition 3.8 of [Adamek] p. 28, and definition in [Lang] p. 54. (Contributed by FL, 9-Jun-2014.) (Revised by Mario Carneiro, 2-Jan-2017.) |
Ref | Expression |
---|---|
df-iso | ⊢ Iso = (𝑐 ∈ Cat ↦ ((𝑥 ∈ V ↦ dom 𝑥) ∘ (Inv‘𝑐))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ciso 17454 | . 2 class Iso | |
2 | vc | . . 3 setvar 𝑐 | |
3 | ccat 17369 | . . 3 class Cat | |
4 | vx | . . . . 5 setvar 𝑥 | |
5 | cvv 3431 | . . . . 5 class V | |
6 | 4 | cv 1541 | . . . . . 6 class 𝑥 |
7 | 6 | cdm 5589 | . . . . 5 class dom 𝑥 |
8 | 4, 5, 7 | cmpt 5162 | . . . 4 class (𝑥 ∈ V ↦ dom 𝑥) |
9 | 2 | cv 1541 | . . . . 5 class 𝑐 |
10 | cinv 17453 | . . . . 5 class Inv | |
11 | 9, 10 | cfv 6431 | . . . 4 class (Inv‘𝑐) |
12 | 8, 11 | ccom 5593 | . . 3 class ((𝑥 ∈ V ↦ dom 𝑥) ∘ (Inv‘𝑐)) |
13 | 2, 3, 12 | cmpt 5162 | . 2 class (𝑐 ∈ Cat ↦ ((𝑥 ∈ V ↦ dom 𝑥) ∘ (Inv‘𝑐))) |
14 | 1, 13 | wceq 1542 | 1 wff Iso = (𝑐 ∈ Cat ↦ ((𝑥 ∈ V ↦ dom 𝑥) ∘ (Inv‘𝑐))) |
Colors of variables: wff setvar class |
This definition is referenced by: isofval 17465 |
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