Timeline for Is there a sensible way to enrich over SymMonCat such that id_X is not the monoidal unit?
Current License: CC BY-SA 2.5
4 events
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| Nov 9, 2010 at 22:16 | comment | added | Theo Johnson-Freyd | Many people use the word "monoidal functor" for "strong" monoidal functors, and mark "lax" or "oplax" as needed. Grammatically, this is formally similar to the habit of using the word "ring" for commutative ring, and "noncommutative ring" for something that may or may not be commutative; see also "noncommutative geometry". | |
| Nov 9, 2010 at 22:10 | comment | added | Mike Stay | Just thought of at least one place I'm going wrong: the monoidal unit in (Ab, $\otimes$) is $\mathbb{Z}$, not the trivial group. Is there a similar tensor product on SymMonCat? | |
| Nov 9, 2010 at 21:27 | comment | added | Mike Stay | Thinking about it some more, I guess I have the same question about Ab-enriched categories, aka ringoids. A one-object Ab-enriched category is a ring; multiplication is composition and addition comes from the abelian group structure. Every object $X$ comes with a group homomorphism from the trivial group to hom$(X,X)$; this preserves the unit and products, so $id_X$ has to pick out the additive identity, not the multiplicative identity. Where am I going wrong? | |
| Nov 9, 2010 at 15:58 | history | answered | Finn Lawler | CC BY-SA 2.5 |