Timeline for "Wrong" strictification of symmetric monoidal categories
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2023 at 5:34 | comment | added | Kevin Carlson | Though it's a decade later, I just thought I might note here that the universal property of many familiar monoidal products Ronnie mentions is nicely formalized in a multicategory, and then one does indeed get all the coherence "for free" out of the universal property. | |
| Apr 24, 2013 at 21:34 | comment | added | Ronnie Brown | In the case of cartesian products, although we can't make the product strict, we get by because the functions to products are always defined by the universal property, and from products by the exponential law. The situation seems analogous for many tensor products because the tensor products are defined by a "bi-" property, like bilinear; similarly for chain complexes, cubical sets, and many others. So we deal without fuss with multilinearity and the associativity of such tensor products. These tensor products seem to be as coherently associative as the usual product. Is this naive? | |
| Apr 24, 2013 at 16:28 | comment | added | Simon Markett | It certainly makes me feel better that I 'only' walked into a trap somebody else already 'set up'. +1 | |
| Apr 24, 2013 at 16:01 | history | answered | Zhen Lin | CC BY-SA 3.0 |