# causality and operationalism:from sets and functions to monads

+ 1 like - 0 dislike
10 views

When working in a laboratory, the most basic behaviour is to turn a knob or dial and then see a transformation of some data output. An example is increasing a magnetic field and seeing zeeman splitting. We normally use this behaviour to create a function, thinking of the system as being composed of a set of states. I am interested in a program which borrows some of the assumptions of quantum gravity. Namely, I am working towards a picture where states are not fundamental, but instead processes are. This leads us to the following picture. We take the turning of the knob as a morphism and the change in the data output as another morphism. The experiment, then, is a map from an arrow to an arrow and this is just an endofunctor on the category of the apparatus. Can we then use this endofunctor to create a monad and subsequently an algrebraic theory for the system under investigation?

This post has been migrated from (A51.SE)
 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverf$\varnothing$owThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.