categorical metaphysics
Say the universe is a category. It is made of some objects whose existence can be perceived by us only through their interactions. A morphism from an object A to an object B contains the information on how A "acts" on B. If this indeed is the universe, what could the perceived universe be like?
1) We can only perceive relations between objects. For instance, the stationary and non-interacting objects is forever undetectable by us. In other words, we only perceive the arrows of the category, not the objects.
2) Moreover, we can not perceive all the arrows. A certain collection of objects and their interactions with each other were irrelevant for our evolutionary history. Hence they are beyond our sensory realm. In other words, there exists a full subcategory that lies outside our perceived universe. Call this subcategory F. (Here "F" stands for the word "forbidden".)
3) The arrows we can perceive do not form a full subcategory. We can detect only some of relationships between A and B, for the same reason as in 2.
Category theory focuses on arrows. Objects are black boxes. This is epistemologically sound. You can not know anything inside out. You do your inquisition from outside in.
Note that the above observations have a nice corollary. We can divide the objects outside F into two classes. Those which are on the periphery P of F and those that are not. Those which are in P have at least one non-empty morphism set with an object from the forbidden subcategory F. (In other words, objects outside F and P have no relationships with F.) This implies that, in our observable world, we may witness actions that emanate from F. (e.g. Observational effects of mirror matter)
1) We can only perceive relations between objects. For instance, the stationary and non-interacting objects is forever undetectable by us. In other words, we only perceive the arrows of the category, not the objects.
2) Moreover, we can not perceive all the arrows. A certain collection of objects and their interactions with each other were irrelevant for our evolutionary history. Hence they are beyond our sensory realm. In other words, there exists a full subcategory that lies outside our perceived universe. Call this subcategory F. (Here "F" stands for the word "forbidden".)
3) The arrows we can perceive do not form a full subcategory. We can detect only some of relationships between A and B, for the same reason as in 2.
Category theory focuses on arrows. Objects are black boxes. This is epistemologically sound. You can not know anything inside out. You do your inquisition from outside in.
Note that the above observations have a nice corollary. We can divide the objects outside F into two classes. Those which are on the periphery P of F and those that are not. Those which are in P have at least one non-empty morphism set with an object from the forbidden subcategory F. (In other words, objects outside F and P have no relationships with F.) This implies that, in our observable world, we may witness actions that emanate from F. (e.g. Observational effects of mirror matter)
