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Do the terms "quiver" and "metagraph" refer to the same concept? Or is there a distinction I am missing.

My sources are

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From Wikipedia: "a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph". Any talk about quivers I've heard starts by explaining that they are just another way of viewing (a general type of) graphs, but that the focus of interest is different from that of graph theorists, whence the different terminology. However I've never heard of a metagraph before, and from the link you provided (which is not very clear) you cannot use a metagraph in place of a quiver (or of a graph), because you apparently are not even allowed to consider its set of vertices (called objects). This is not so much because they might be too numerous to be a set (like when they would form a set-theoretic proper class), but because the theory in question is not founded in set theory in the first place.

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    I'm abandoning this discussion; we don't seem to communicate. I'l just list some problems I have: (a) your graph article says (conditionally) morphisms are _functions_ based on NOTHING, (b) I'm not enough of a logician to appreciate "not dependent on set theory" claims, I thought at least Hom$(X,Y)$ is a set, (c) "[0..*]" mystifes me, (d) what you list doesn't even look remotely like axioms ("has objects", "connect objects" Huh? This is not even in the language) and there is nothing one could imagine deducing from them.2012-08-21