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The two ways Feynman diagrams appear in mathematics

If I understand the question correctly, the search is for a calculation of the asymptotic expansion of Gaussian integrals using concepts and techniques from category theory. Here is one such ...
• 152k

String diagrams for bimonoidal categories (a.k.a. rig categories)?

This question is answered in the affirmative in the following preprint: Cole Comfort, Antonin Delpeuch, Jules Hedges, Sheet diagrams for bimonoidal categories, arXiv:2010.13361 The morphisms are ...
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Accepted

Monoidal category that is not spacial

One of the simplest examples of a non-spacial category is $\mathrm{End}(\mathrm{Vec}^{\oplus 2})$, the category of $2\times2$ matrices with vector space coefficients. Working over a field $\mathbb k$, ...
• 49.9k
Accepted

String diagrams for bimonoidal categories (a.k.a. rig categories)?

There isn't anything like a graphical calculus really expressly dedicated to rig categories, and well-documented and proved to be coherent, but there are 'approximations' to what you are looking for: ...
• 5,833

The two ways Feynman diagrams appear in mathematics

Before interpreting them in more advanced language like "string diagrams" or "monoidal closed categories" it might be good to stress that Feynman diagrams are very elementary combinatorial objects ...

• 49.9k

Singularity-free isotopies between string diagrams for monoidal categories

If I understand your question correctly, it seems that there is a problem of winding numbers. Your diagrams seem to allow ending on univalent vertices. Consider, then, a string that starts at a ...
• 49.9k

Monoidal category that is not spacial

An example I learned about in Khovanov's "Heisenberg algebra and a graphical calculus", 2010, is the restriction and induction functors for the infinite chain $S_0\subset S_1\subset S_2\subset\cdots$ ...
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