Timeline for Monoidal categories whose tensor has a left adjoint
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2021 at 19:03 | history | edited | varkor | CC BY-SA 4.0 |
added 596 characters in body
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| Jan 5, 2021 at 12:29 | comment | added | Tim Campion | Er -- rather, that other question is not-so-tangentially related -- it's the dual of the special case where the monoidal structure is cocartesian. | |
| Jan 5, 2021 at 0:00 | vote | accept | varkor | ||
| Jan 4, 2021 at 2:00 | history | became hot network question | |||
| Jan 3, 2021 at 23:04 | answer | added | Tim Campion | timeline score: 20 | |
| Jan 3, 2021 at 21:12 | comment | added | Tim Campion | Reminds me of a tangentially related question. | |
| Jan 3, 2021 at 21:01 | answer | added | Qiaochu Yuan | timeline score: 22 | |
| Jan 3, 2021 at 20:55 | comment | added | Noah Snyder | @QiaochuYuan: Ah, right. In my setting, one looks at the Deligne-Kelly tensor product of the two categories rather than their Cartesian product, and so the functor out of that is also right exact. | |
| Jan 3, 2021 at 20:49 | comment | added | Qiaochu Yuan | @Noah: usually tensor product is right exact in each argument; varkor is asking for an adjoint of the entire functor of two arguments, not an adjoint in one argument or the other. | |
| Jan 3, 2021 at 20:47 | comment | added | Noah Snyder | This probably won't help you. What I'm familiar with is a related question which is when the right adjoint (which usually automatically exists under the assumptions people typically work in for tensor categories) has the structure of a strong module functor. See Section 4.1 of arxiv.org/pdf/1804.07538.pdf and Appendix D of people.math.harvard.edu/~gaitsgde/GL/shvsofcat.pdf | |
| Jan 3, 2021 at 20:36 | comment | added | varkor | @NoahSnyder: the concept is intended to be a weakening of the notion of cartesian category (where the cartesian product is right adjoint to the diagonal). However, one could just as well ask for a right adjoint instead, which would correspond to the cocartesian setting. I'm happy to know of references for either. | |
| Jan 3, 2021 at 20:28 | comment | added | Noah Snyder | Usually tensor product is right exact, not left exact. Are you sure you want to be asking for a left adjoint here and not a right adjoint? | |
| Jan 3, 2021 at 17:57 | history | asked | varkor | CC BY-SA 4.0 |