Timeline for Are all binoidal categories (in the literature) actually strict?
Current License: CC BY-SA 2.5
8 events
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| Apr 2, 2011 at 20:12 | comment | added | Adam | @Buschi, yes, a binoidal category B looks a bit like a quasi-functor B×B→B, except it doesn't have the 2-cell $\gamma_{f,g}$ (which would be from the first math display of my question to the second)... unfortunately, leaving that out is what makes binoidal categories useful in modeling of effects. But thanks for pointing out the connection! | |
| Apr 2, 2011 at 19:54 | history | edited | Adam | CC BY-SA 2.5 |
make the last bit a "side note"
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| Apr 2, 2011 at 19:47 | history | edited | Adam | CC BY-SA 2.5 |
clarify the two additional questions I really care about, which were implicit (but should have been explicit) in the original posting
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| Apr 2, 2011 at 17:18 | comment | added | Adam | Yes Finn, I'm sure. Look carefully at the Power+Robinson paper: they don't actually say which functors the associator establishes a natural isomorphism between -- they only give the domain and codomain of its components, and this is somewhat ambiguous because the "action on objects" notation for the left-product and right-product functors is the same. You have to work backwards to figure out the actual functors which are naturally isomorphic; these turn out to be the ones in the last display of my question. | |
| Apr 2, 2011 at 16:29 | answer | added | Todd Trimble | timeline score: 1 | |
| Apr 2, 2011 at 14:32 | comment | added | Finn Lawler | Are you sure that your last isomorphism is the associator? It seems to me (looking at Power and Robinson's paper) that the associator does exactly what you want. Incidentally, I don't think there's any reason why binoidal categories proper should obey your axiom in general. | |
| Apr 2, 2011 at 11:08 | comment | added | Buschi Sergio | I his work "Formal Category Theory: Adjointness for 2-Categories, Lecture Notes in Mathematics 391" J.W Gray define the notion of quasi-functor on two variables (p. 56), and this is a family of (2-) funtors that resemble a bit the binoidal category axiom. Then Gray come to define a monoidal structure on 2-Cat (different from the cartesian one) we call it $(2-CAt, \bigotimes)$, and the tensor product is a quasi-functor (on two varibles), and from tha top diagram p. 57 I seems that this can help you | |
| Apr 2, 2011 at 3:13 | history | asked | Adam | CC BY-SA 2.5 |