Free Objects and Tensor Products of Modules over a Commutative Ring
نویسنده
چکیده
If you have taken a standard abstract algebra course, then you have probably heard of free groups. But, most such courses do not introduce the reader to the language of category theory, which unifies the notion of a free object. In the present lecture, we will define a free group categorically, and then go on to define a free module over a commutative ring, and hence, a free abelian group (which is just a Z–module). For present purposes, we will assume that free groups exist (if you are curious, just pick up any standard abstract algebra textbook and take a look at the construction of a free group).
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