Timeline for Tensored Over Abelian Groups?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2009 at 19:22 | comment | added | Mariano Suárez-Álvarez | @Manny: The object is unique, because it represents the functor $Y\mapsto\hom_{\mathrm{Ab}}(A,\hom_C(X,Y))$. | |
| Dec 9, 2009 at 19:21 | comment | added | Manny Reyes | I like this definition for the tensor product! It's uniquely determined by Yoneda's Lemma, correct? (I just want to check that I'm not missing something important.) | |
| Dec 9, 2009 at 17:40 | comment | added | Chris Schommer-Pries | In certain contexts "biproduct" can have a different meaning (e.g. in the context of bicategories). But arguing over terminology is a little ridiculous. The main point is that this is a beautiful answer. | |
| Dec 9, 2009 at 17:07 | comment | added | Qiaochu Yuan | There's already a term for something which is simultaneously a product and a coproduct: biproduct. | |
| Dec 9, 2009 at 15:47 | comment | added | Leonid Positselski | "Direct sum" and "coproduct" (in an additive category) are the same thing for me. I thought it was the standard terminology. As to the product and the coproduct of an infinite number of copies of a certain object, these two never coincide in an abelian category, unless the object is zero. | |
| Dec 9, 2009 at 15:00 | comment | added | Chris Schommer-Pries | I thought of this as I was writing the question, but wanted to see what other people would say, anyway. When you say "infinite direct sum" you mean coproduct, right? When I hear "direct sum" I usually think something which is simultaneously a product and a coproduct. Even for the category of abelian groups infinite direct sums in that sense don't exists. | |
| Dec 9, 2009 at 14:54 | vote | accept | Chris Schommer-Pries | ||
| Dec 9, 2009 at 14:02 | history | answered | Leonid Positselski | CC BY-SA 2.5 |