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Full names are often not (in fact ore often than not) given in the publication data so a copy and paste of a reference ends up without the full names.(Of course, ideally one can add in fuller form later on.) I do not understand why in papers the full name is usually not used.
I wholeheartedly agree about ‘legacy’.
In fact it is not extra work to hide those names, it is extra work for find full names. :-)
Yes, we need not follow the weird traditions in print publication of tending to make following citations a detective story – such as not identifying authors completely, not giving titles (standard in parts of physics!) and (nowadays) not giving url-s. Let’s provide all this data!
I agree … where we can find it!!!!! It took mequite some time to find Laurent Regier’s homepage. A google search gave lots of derivative pages, (Researchgate, etc.) but the Google weighting of his personal web page must have been low, at least that is what I presume.
Added a reference to a 2020 paper.
Thanks.
I added a couple of links: chain rule and Leibniz rule. The latter redirects to Leibniz algebra, not so clear the connection to the rule. [EDIT: But there is equation (1) there]
It would be good to have a few words on why those diagrams do what they say,e.g., chain rule.
And we ought to have first a definition of ’differential category’.
Also, is there a reference for codifferential categories?
Explanation of the differences between differential and codifferential categories. Example of $Vect_{\mathbb{K}}$ and formal polynomials. I’ve explained what the diagrams mean in the definition of the derving transformation.
For the forum: In the references, the notion of differential category is used and they say for the specific examples that this category $\mathcal{C}$ is such that $\mathcal{C}^{op}$ is a differential category, ie. it is a codifferential category rather than giving directly the definition of a codifferential category.
However in a recent paper, Jean-Simon have given directly the definition of a codifferential category (“Why FHilb is Not an Interesting (Co)Differential Category” and “”). At FMCS 2022, Sacha Ikonicoff used the codifferential setting with his presentation titled “Cartesian Differential Monads” (https://pages.cpsc.ucalgary.ca/~robin/FMCS/FMCS2022/slides/Sacha.pdf), however Jean-Simon wrote the definition of a cartesian codifferential monad in the paper (https://arxiv.org/pdf/2108.04304.pdf), this is another structure than differential categories but this is the same problem.
Codifferential definitions are more intuitive for mathematicians because monads and monoids are more natural for us than comonads and comonoids but linear logic and differential linear logic are based on the differential definition. This is why Sacha like me, we prefer the codifferential definition but Jean-Simon which has been the main contributor during the preceding years want to stay close to linear logic.
A lot of categories are at the same time differential categories and codifferential categories, for example the $*$-autonomous differential categories, and this fact seems to be linked to distributions. I’m starting to disuss of this with Jean-Simon and Marie Kerjean who is more into differential linear logic and concrete models. I hope to come back with theorems to write on the nlab. Definitely differential categories are still under development.
Jean-Baptiste Vienney
Added related page link to tangent bundle category, which I think is more appropriate than tangent category.
I agree. I find it better after your edit.
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