Timeline for Inducing a Monoidal Structure using an Equivalence of Categories
Current License: CC BY-SA 3.0
10 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jun 13, 2014 at 1:07 | comment | added | user62675 | @ZhenLin Yes, I found Martin Brandenburg's comment here. I forgot to cite it; I apologize for that. I have added it into the answer. Again, I apologize for forgetting to cite it. | |
| Jun 13, 2014 at 1:05 | history | edited | user62675 | CC BY-SA 3.0 |
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| Jun 13, 2014 at 1:02 | comment | added | Zhen Lin | (1) You're quoting Martin Brandenburg. (2) I have yet to see an explicit definition of the so-callled "proper language of categories". | |
| Jun 12, 2014 at 22:42 | history | edited | user62675 | CC BY-SA 3.0 |
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| Jun 12, 2014 at 22:40 | comment | added | user62675 | @QiaochuYuan Strict monoidal categories are not definable in the (proper) language of categories. (Strict monoidal categories belong instead in set theory.) See my edit incorporating that into the answer. | |
| Jun 12, 2014 at 21:55 | history | edited | user62675 | CC BY-SA 3.0 |
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| Jun 12, 2014 at 21:03 | comment | added | Qiaochu Yuan | The first statement should be false if not interpreted carefully. For example, it shouldn't be true that you can transport a strict monoidal structure to another strict monoidal structure along an equivalence of categories, although I don't know an explicit counterexample. The analogous statement in homotopy theory is that you shouldn't be able to transport a strictly associative multiplication to another strictly associative multiplication along a homotopy equivalence. So there is really something to check here, namely that the usual definition of a monoidal category is weak enough. | |
| Jun 12, 2014 at 21:02 | history | edited | user62675 | CC BY-SA 3.0 |
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| Jun 12, 2014 at 20:53 | history | answered | user62675 | CC BY-SA 3.0 |