Timeline for Cartesian product is to monoidal product as pullback is to what?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 27, 2021 at 17:05 | comment | added | Tim Campion | My answer over here is in principle applicable here, too, but I'm not sure what exactly the conclusion ends up being. | |
| Dec 21, 2021 at 23:05 | comment | added | vikraman | What archetypal examples do you have in mind? If you're willing to consider symmetric monoidal instead of monoidal structure, I can point you to local independent (co) products, which seem to be a useful axiomatisation of fibred symmetric monoidal structure that I learned about recently: coalg.org/mfps-calco2017/mfps-papers/6-simpson.pdf | |
| Dec 21, 2021 at 17:11 | comment | added | D.-C. Cisinski | Conclusion: the notion of pullback is an instance of a composition law for $1$-cells in a bicategory. This specializes to cartesian products as a monoidal product when we restrict to the point. | |
| Dec 21, 2021 at 12:58 | comment | added | D.-C. Cisinski | Maybe it is a 2-category (or a variation on such concept, such as a bicategory): products are pullbacks over a prescribed object, namely the terminal one, whereas a monoidal category is bicategory with a single object. If we want products over a variety of objects (=pullbacks), the "monoidal counterpart" would be a bicategory with many objects. In short, pullbacks define the bicategory of spans. | |
| Dec 21, 2021 at 0:04 | comment | added | David Roberts♦ | A monoidal category such that all its slices/coslices inherit a monoidal structure? Hmm.. | |
| Dec 20, 2021 at 23:29 | history | asked | Bruno Gavranovic | CC BY-SA 4.0 |