Timeline for Has anyone heard of a Lax Monoidal Functor where one of the arrows is flipped?
Current License: CC BY-SA 4.0
12 events
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| Aug 24, 2023 at 21:55 | comment | added | José Alvim | Thank you, @PeterLeFanuLumsdaine. Yes, there is a comparison between $F\bigotimes^n_{i=1} A_i$ and ${\bigotimes'^{~n}_{j=1}}F A_j$ for every $n$. It just so happens that this comparison is “the wrong way around” when n = 0. | |
| Aug 4, 2023 at 9:49 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |
fixed broken nlab link (while question is already bumped from retagging)
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| Aug 4, 2023 at 9:33 | comment | added | Peter LeFanu Lumsdaine | Following @MaximeRamzi’s second comment: In situations like this, it’s almost always useful to think about $k$-ary tensor products $A_1 \otimes \cdots \otimes A_k$ for general $k \in \mathbb{N}$, not just the special cases $k=0,2$. Usually, the correct abstraction of some situation can be described uniformly for all $k$ — e.g. an oplax monoidal functor has maps $F(A_1 \otimes \cdots \otimes A_k) \to FA_1 \otimes \cdots \otimes FA_k$. Does your situation have any general comparison between $A_1 \otimes_c \cdots \otimes_c A_k$ and $A_1 \otimes_{c'} \cdots \otimes_{c'} A_k$? | |
| Aug 4, 2023 at 9:11 | history | edited | varkor |
edited tags
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| Jun 12, 2022 at 22:51 | history | edited | José Alvim | CC BY-SA 4.0 |
added 86 characters in body
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| Jun 12, 2022 at 16:10 | comment | added | Maxime Ramzi | I see. It is a bit surprising (although of course if that's your situation, that's your situation) because the unit can be viewed as a nullary tensor product, which is why these things usually go in the same direction . So I don't think this has been studied | |
| Jun 11, 2022 at 16:26 | comment | added | José Alvim | Thank, you Ramzi. But yes, I'm aware. Unfortunately the arrows go in opposite directions to each other so neither applies. | |
| Jun 11, 2022 at 9:35 | comment | added | Maxime Ramzi | Just in case : if the map between units was in the other direction, you would get an oplax monoidal functor | |
| Jun 11, 2022 at 6:23 | history | edited | José Alvim | CC BY-SA 4.0 |
Okay I think _now_ it's correct, jeesh
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| Jun 11, 2022 at 5:16 | history | edited | José Alvim | CC BY-SA 4.0 |
edited title
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| S Jun 11, 2022 at 5:15 | review | First questions | |||
| Jun 11, 2022 at 11:27 | |||||
| S Jun 11, 2022 at 5:15 | history | asked | José Alvim | CC BY-SA 4.0 |