I am working on free objects, I am restricting myself primarely to groups, rings and modules (with maybe algebras) so in a sense in the concrete category (if I am not mistaken. This is a thesis work I am doing and as such references is of outmost importans, and I found this note document which gave an interesting definition of free objects which I'll cite
A free object is the mother of all objects of that type, in the sense that every object of that type is a quotient of the free object
This is an extremely good definition for what I am after, especially when you comapare it with this definition which I have seen many times before. I don't include the diagram or that one becuase I do not know how to draw a diagram on here. However I curious, does anyone know a good source for the first definition? Or how to prove it from the more common definition?