MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-cic Structured version   Visualization version   GIF version

Definition df-cic 17779
Description: Function returning the set of isomorphic objects for each category 𝑐. Definition 3.15 of [Adamek] p. 29. Analogous to the definition of the group isomorphism relation ≃𝑔, see df-gic 19214. (Contributed by AV, 4-Apr-2020.)
Assertion
Ref Expression
df-cic ≃𝑐 = (𝑐 ∈ Cat ↦ ((Isoβ€˜π‘) supp βˆ…))

Detailed syntax breakdown of Definition df-cic
StepHypRef Expression
1 ccic 17778 . 2 class ≃𝑐
2 vc . . 3 setvar 𝑐
3 ccat 17644 . . 3 class Cat
42cv 1533 . . . . 5 class 𝑐
5 ciso 17729 . . . . 5 class Iso
64, 5cfv 6548 . . . 4 class (Isoβ€˜π‘)
7 c0 4323 . . . 4 class βˆ…
8 csupp 8165 . . . 4 class supp
96, 7, 8co 7420 . . 3 class ((Isoβ€˜π‘) supp βˆ…)
102, 3, 9cmpt 5231 . 2 class (𝑐 ∈ Cat ↦ ((Isoβ€˜π‘) supp βˆ…))
111, 10wceq 1534 1 wff ≃𝑐 = (𝑐 ∈ Cat ↦ ((Isoβ€˜π‘) supp βˆ…))
Colors of variables: wff setvar class
This definition is referenced by:  cicfval  17780
  Copyright terms: Public domain W3C validator