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Stream: deprecated: our papers

Topic: Inner autoequivalences in general and those of monoidal c...

Martti Karvonen (May 10 2022 at 00:45):

Like I mentioned in the other thread, me and Pieter Hofstra were just about to finish a draft before he died. I have now incorporated his comments and posted the end result on arXiv.

Martti Karvonen (May 10 2022 at 00:45):

In a nutshell, the main goal is to prove the following theorem: inner autoequivalences of a monoidal category $\mathcal{C}$ are of the form $X\otimes - \otimes Y$ where $X\otimes Y\cong I\cong Y\otimes X$. More precisely, the 2-group of inner autoequivalences of a monoidal category is equivalent to its Picard 2-group.

Martti Karvonen (May 10 2022 at 00:49):

For this to be a theorem and not a definition, one needs a general theory of inner autoequivalences of an object in a 2-category. There is such a theory, and we spend some time developing it. This generalizes an existing theory (see e.g. this or this) of inner automorphisms to the two-dimensional setting. A key technical tool is given by conveniently chosen dense subcategories: they make things tractable by letting one compute with smaller amounts of data.