20/04/12 13:22:51 hAg37Ryy.net
>>25
つづき
Conclusion
These notes have attempted to cast some of the examples proposed by Mochizuki to answer Scholze?Stix’s concerns in a more category-theoretic light. Ideally all discussions about the content of IUTT can be addressed in such precise terms,
rather than worry about things like “the risk that different people will “remember” different labeling appartuses [sic], which result in structurally non-equivalent mathematical structures”, Report (DfLb)
By replacing discussion of psychology and suggestive metaphors by rigorous definitions of all the categories in which objects live, and keeping track of forgetful functors, communication about IUTT can focus on the difficult mathematical content, rather than about whether or not objects need specific labels.
Addendum, 22 October
After giving the matter more thought, I came to the realisation that Mochizuki is using a subtly different definition of diagram than that which is commonly accepted. In the example ‘colimits and diagrams’ above, we had the diagram
(引用終り)
以上