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started adding list of references to the page Bill Lawvere
not that I made it very far -- just three items so far :-)
I was really looking for an online copy of "Categorical dynamics" as referenced at synthetic differential geometry and generalized smooth algebra, but haven't found it yet. I was thinking that the "Toposes of laws of motion" that I do reference must be something close. But I don't know.
I added a link to a web page that has a copy of Lawvere’s “Perugia notes”.
Oh, fantastic, Mike! I’ve long wanted to have a look at those.
Thanks for the pointer. I hadn’t seen that before. Happy to find that it matches well with variational calculus – In terms of smooth spaces.
Concerning the pullback alluded to on the very last page which constrains the domain of variation, I take that as occasion to advertize what I find a pleasant effect of formalized cohesion on variational calculus:
for the typical variational calculus on functionals on spaces of maps $\Sigma \to X$ out of a manifold $\Sigma$ with boundary and with boundary data held fixed (this includes all the variational problems in classical physics) the domain is the pullback
$(X^\Sigma)_{var} \coloneqq X^\Sigma \underset{X^{\partial \Sigma}}{\times} \flat (X^{\partial \Sigma}) \,,$where “$\flat$” is the modality of discrete cohesion.
I added the Perugia reference to variational calculus.
Thanks, Zoran. I had wanted to do that last night, but then my battery died and my train stopped :-)
I have expanded the comment line above the reference as follows:
A perspective on variational calculus in terms of internal hom mapping spaces in a context of cohesion along the lines discussed above has been indicated in…
I have also tried to organize the References-section a bit more. But it’s always hard to do so.
The Perugia notes are really nice! His introduction to his philosophy of sets is one of the strongest argument I’ve seen for structural foundations.
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