I'm trying to understand some fundamental concepts of abstract algebra and, since i'm not a mathematician but a math enthusiast, i'm having some difficulties establishing connections.
A morphism should be a function among two algebric structures preserving the operations defined in them. A linear function should be pretty much the same, considering structures where, usually, operations aren't different. And here comes the doubt. A multilinear function generalizes the linearity concept, applying it "variable-wise" to multivariable functions. Is there, accordingly, any kind of generalization of a morphism? Is there any unifying concept able to embrace both as particular cases?
I'm asking since a multivariable function can also be treated linearly, considering the n-tuple of variables as a single element and, thus, applying the linearity concept to it.
I trying to figure which piece of the puzzle i'm missing.