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[dreyonlegacy]

Of "vital" importance:

Is there an injection of hom(x^3,x) into (hom(x^2,x))^2? I.e. given a map D(x,y,z), can I decompose this into A(B(x,y),z)? I need to make sure that my conjunctions actually work.
It looks like it should work, but I want to make sure that there isn't something really bizarre lurking around.

Comments

[sniffnoy]

What's meant by "hom" here, and what's X? Is this just in the category of sets? If so you appear to have done something wrong

[dreyonlegacy]

I don't really need the correspondence to be natural in the least, I just need it to exist. And X is definitely infinite, containing the set of all conjugations of its elements.
Basically, the question I was trying to ask was: am I allowed to specify that all single conjunctions take two arguments without losing the possibility of representing a conjunction that takes n arguments, for n > 2?
As long as the correspondence exists in some form I'm happy. It'd be nice if it were natural, but I wasn't really expecting that.