20/04/12 14:00:27 hAg37Ryy.net
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The Scholze?Stix simplifications
So given all this discussion of peculiarities on Mochizuki’s side, what can be said about the approach of Scholze?Stix?
Many times they say they are identifying certain objects of interest that are known to be isomorphic/equivalent. Mochizuki objects to this,
but it is not a priori clear that identifying objects is destructive: in the examples above of colimits, one did not need to ensure that different objects were the values of different nodes in the diagram shape.
The book-keeping is taking place at the diagram level, not at the specific identity of the objects.
However, one can go too far in this process. Recalling the discussion in the section ‘Category theory and structuralism’ above,
one may identify objects X or X’ assuming one has a given isomorphism between them, or else choosing a specified isomorphism
b : X ～→ X’.
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