/sci/ - Science & Math

>>9778609
>>9778615
None of these are related to tensor factors of derivation modules, of which functions with differential operators are an example of. This is one of those cases where different math objects are assigned the same name. Please don't confuse >>9778562 and >>9778600 with your ignorance.

In general in a monoidal category C, you can equip it with a tensor structure, which can be treated as a map C x C → C that is natural with respect to the monoidal structure. The universal property is that, if an object V is isomorphic in C to a tensor product if objects W and Z, then endomorphisms of V are isomorphic to a tensor product of endomorphisms on W and Z.
Let C be the category of derivation modules over manufolds, I.e. its objects are modules of functions M on a manifold X equipped with an action by a derivation algebra A of differential operators, and its morphisms are modules morphisms. Then C is a symmetric monoidal tensor category (check!). If X has separable coordinates, then M is a tensor factor of modules of functions and the a-evaluation endomorphism for a in A has the universal property.
>>9778633
Again, this has absolutely nothing to do with PDE's, which lies beyond the scope of linear algebra. Please stop trying to sound smarter than you actually is.

>>9380912
>tangential

>>8957345
Just finished a MSc.
I'll be leaving soon for a PhD elsewhere and I don't want to start a project with someone I won't be able to meet regularly. Leaves a bad taste in my mouth.
I'll probably look at this problem more seriously in the future while doing my PhD desu.
>>8957353
Well then maybe I'll pay him a visit.