Jun 18
I think that all the data of a theory of scissors congruence might be able to be captured in a single morphism of topoi... Stay tuned I guess
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seen from China
I think that all the data of a theory of scissors congruence might be able to be captured in a single morphism of topoi... Stay tuned I guess
Need to finish this section of my research notes so I never have to write 'associated strict tomomorphism functor' ever again
Conversations with my thesis advisor are always so nice. Today we proved that even in 1-dimensional scissors congruence, any figure of positive volume has scissors congruences of infinite order (group-theoretically), so if you keep composing them with themselves you never get back the identity transformation.
Preserving covers and pullbacks is sufficient to induce a unique functor betweens scissors categories, but it's certainly not necessary...
Watch out people! This is Serious Mathematics for Seriously Smart People only ... also it's on the level of Kindergarten.