---
date: 2023-05-11 00:00:00
---
multiple file formats


- heterogenous decentralisation
- cats is about objects which are processes, making them deployable as infrastructure
- processes are blocks. cats, like blocks, do not care what the objects being processed are
- RIDs for CARs? (is this RIDs for identity too?)
	- how to represent and deploy inter-systemic (Identity) relations
- are relations the same as blocks? are they a superset? subset?
- to Z: how would a non-process relation be represented as a block? i.e. relations
	- symmetric blocks? 
- content-addressed files form a network of acyclical reference

portable relations & (RIDs for) content-addressed relations
```
RID[CID] -> {
	relation: RID (Identity)
	relata: set | (set, set)
}
```

```
Add -> {
	relation: AddBlock
	relata: [
		space_1,
		space_2
	]
}

ReduceDimensions -> {
	relation: ReduceDimensionsProcess
	relata: {...}
}

Isomorphic -> {
	relation: Isomorphism
	relata: {...}
}
```

```
Identity -> {
	relation: Identity
	relata: {O1, O2, ..., On}
}
```

Identity and symmetric functions

$C(S, D) \land \forall O_1, O_2 \in \text{Identity}: S(O_1, O_2) \land (O_1 \neq O_2 \rightarrow D(O_1, O_2))$

- $S(f, g) \equiv \forall x \in \text{Domain}(f) \cap \text{Domain}(g): f(x) = g(x)$

$S((f_1, g_1), (f_2, g_2)) \equiv \forall a \in \text{Domain}(f_1) \cap \text{Domain}(f_2): g_1(f_1(a)) = a = g_2(f_2(a))$ and $\forall b \in \text{Domain}(g_1) \cap \text{Domain}(g_2): f_1(g_1(b)) = b = f_2(g_2(b))$.