Timeline for Monoidal structure on a category with products and with terminal object
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2012 at 17:37 | vote | accept | Sergei Akbarov | ||
| Nov 2, 2012 at 7:26 | answer | added | Buschi Sergio | timeline score: 5 | |
| Nov 1, 2012 at 23:15 | comment | added | David Roberts♦ | @Sergei, using the Yoneda lemma it is, because that tells you the functor $X\mapsto Hom(-,X)$ is fully faithful. | |
| Nov 1, 2012 at 22:53 | answer | added | David Roberts♦ | timeline score: 8 | |
| Nov 1, 2012 at 20:20 | comment | added | Sergei Akbarov | Sergio, I don't understand this trick. Is it possible, for example, to prove the diagram of associativity (the pentagon) in this way? | |
| Nov 1, 2012 at 20:03 | comment | added | Buschi Sergio | Is easy (elements check) that $Set$ is cartesian (i.e. for finite products) monoidal, then for a general cartesian category you apply the (general) representable $(X, -)$ to the axioms diagrams (and use the result in $Set$), then the commutativity of each diagrams follow from Yoneda Lemma (need only the faithful part). | |
| Nov 1, 2012 at 20:00 | comment | added | Sergei Akbarov | Eric, thank you, that's interesting. So this means that the accurate proof exists... It would be nice to look at it... | |
| Nov 1, 2012 at 19:57 | answer | added | Wouter Stekelenburg | timeline score: 2 | |
| Nov 1, 2012 at 19:41 | comment | added | Eric Peterson | I don't know a reference, but I do know this has a name: ncatlab.org/nlab/show/cartesian+monoidal+category . | |
| Nov 1, 2012 at 19:13 | history | asked | Sergei Akbarov | CC BY-SA 3.0 |