Ontology of Memoidealism

We devised ontology of Memoidealism based on mathematics, on category theory⁴¹. It is a hierarchy of categories which consists of collections of objects and arrows between them. We chose category theory instead of set theory for our ontology in order to have the concept of Time represented intrinsically by arrows which are a part of any category. The first level is a simple MemS category of memuons as memory objects and arrows between them:

Metaphorically this can be considered as a single memory state. The next level is a MemL category with MemS objects and arrows between them. This is essentially a functor and it can be considered as a single memory line or memory life constructed from memory states:

The next level is a functor category⁴² MemW with MemL functors and natural transformations between them. It can be considered as a single memory world constructed from memory lines (or lives):

Going higher there is also MemU category of memory worlds and it can be considered as a memory universe and even higher categories of memory universes.

⁴¹ https://en.wikipedia.org/wiki/Category_theory

⁴² https://en.wikipedia.org/wiki/Functor_category