So like, can you use morphisms to map paths described in one graph to paths described in another graph even if the nodes are different or loosely defined? (eg a functor from one graph to another that creates paths all the nodes that are tagged as “high probability” or all the nodes that have “connectivity matrix exceeding X” to a second graph that is very different from the first graph but which has nodes that still can be ordered by connectivity and have connectivity values that may exceed X?) Where X may be a fixed number or a number that scales according to the dimension of the graph?
Like, I can try to plot out my “weird learning strategy” whenever I enter new environments and I can maybe construct a path that maps out this “weird learning strategy” (focus on highly connected clusters that already have lots of information outputted, focus on nodes that are not individually overwhelming, focus on nodes that already have some connectivity with my own original graph [the possible relationships/morphisms between my graph and that of environment1 and environment2 are different—however—they’re still enough to impose some kind of structure that can be used to establish morphisms between me+environment1 and me+environment2])
==
==
Also, aren’t real world categories so murky that any morphism between two categories is loosely rather than absolutely defined? [eg [in paths you execute comparing one to the other you will expect that your morphisms will be wrong some X percent of the time]]. I would expect that maybe your own graph/category corresponds to your own “world model” and you might be trying to create a new beahvioral graph/path for a new person where you map your world model to that of another person [where some nodes are missing] and specify them to take actions that are contrary to the actions you do?
So like, can you use morphisms to map paths described in one graph to paths described in another graph even if the nodes are different or loosely defined? (eg a functor from one graph to another that creates paths all the nodes that are tagged as “high probability” or all the nodes that have “connectivity matrix exceeding X” to a second graph that is very different from the first graph but which has nodes that still can be ordered by connectivity and have connectivity values that may exceed X?) Where X may be a fixed number or a number that scales according to the dimension of the graph?
Like, I can try to plot out my “weird learning strategy” whenever I enter new environments and I can maybe construct a path that maps out this “weird learning strategy” (focus on highly connected clusters that already have lots of information outputted, focus on nodes that are not individually overwhelming, focus on nodes that already have some connectivity with my own original graph [the possible relationships/morphisms between my graph and that of environment1 and environment2 are different—however—they’re still enough to impose some kind of structure that can be used to establish morphisms between me+environment1 and me+environment2])
==
==
Also, aren’t real world categories so murky that any morphism between two categories is loosely rather than absolutely defined? [eg [in paths you execute comparing one to the other you will expect that your morphisms will be wrong some X percent of the time]]. I would expect that maybe your own graph/category corresponds to your own “world model” and you might be trying to create a new beahvioral graph/path for a new person where you map your world model to that of another person [where some nodes are missing] and specify them to take actions that are contrary to the actions you do?