Timeline for Why does abelianization preserve finite products, really?
Current License: CC BY-SA 4.0
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| Mar 11, 2021 at 19:14 | comment | added | Dario Stein | Thank you Paul, for the special case of abelianization you gave a great intuition. Though you seems to be using the trick that for groups, the product is actually a quotient of the coproduct. This is strange categorically. In order to even define $G * H \to G \times H$ one needs unitality/zero objects again. | |
| Mar 11, 2021 at 17:46 | comment | added | Paul Taylor | Sorry, I only read half of this long question and thought I could give a quick answer just before logging off and going out. The more general question is more interesting and not obviously one for a categorist. I wonder whether my argument might give a hint. | |
| Mar 11, 2021 at 12:01 | comment | added | Carl-Fredrik Nyberg Brodda | Group theorists call the coproduct the free product, which in turn is distinct from (what you might be thinking of) a free product with amalgamation. | |
| Mar 11, 2021 at 11:29 | history | answered | Paul Taylor | CC BY-SA 4.0 |