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1 vote

Reference for free symmetric monoidal categories with duals on symmetric monoidal categories

I thought the autonomization construction can be generalized to the symmetric case, and had a go at writing up the construction: https://arxiv.org/abs/2201.07527 However it does not work, because of a …
pintoch's user avatar
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2 votes

Singularity-free isotopies between string diagrams for monoidal categories

This conjecture was confirmed recently, with two different methods: By Jamie and I, as a corollary of our work on the word problem for monoidal categories (in which we give algorithms to detect wheth …
pintoch's user avatar
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3 votes

Branching behavior in string diagrams/monoidal categories?

You can represent such a branching behaviour in bimonoidal categories (also known as rig categories). In addition to your multiplicative monoidal structure $\otimes$, which is used to represent compou …
pintoch's user avatar
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9 votes
2 answers
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Why is a braided left autonomous category also right autonomous?

In Selinger, P. A survey of graphical languages for monoidal categories (New Structures for Physics, Springer, 2011, 813, 289-233), it is stated that: Lemma 4.17 ([23, Prop. 7.2]). A braided monoi …
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