category theory in number theory

category theory in number theory

[Urs Schreiber]

Dear category theorists,

in a recent note, David Roberts makes a curious point about the
unsettled debate between Mochizuki and Scholze-Stix, who, as you will
have heard, do not agree either on Mochizuki's proposed proof of the
abc-conjecture, nor on Scholze-Stix's proposed rebuttal of that proof.

David points out that the sticking points, at least of that latest
exchange, are not in hard number theory but... in basic category
theory.

See his announcement here

   thehighergeometer.wordpress.com/2018/09/28/on-mochiukis-report-on-discussions/

with a link to the 7-page note here:

   thehighergeometer.files.wordpress.com/2018/09/mochizuki_final1.pdf

This walks the reader through some examples in Mochizuki's arguments,
pointing out how basic category theory seems to be the toolboox
missing here.

This might be an interesting point for interested category theorists
to explore further. If David is right about his analysis of
Mochizuki's latest "Report", then the whole of his series of articles
in the IUTT-series would still be waiting for somebody to go through
from a category theorist's perspective.


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