Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Forgot to sign in again - that was me.
Since SDT is an extension of SDG
By synthetic differential topology (SDT) we shall understand an extension of synthetic differential geometry (SDG) obtained by adding to it axioms of a local nature—to wit, germ representability and the tinyness of the representing objects… which are logical, rather than algebraic infinitesimals. To those, we add four postulates, (excerpt)
perhaps we might expect the same advantages for a germ-based differential cohesion over SDT, as jet-based differential cohesion over SDG
A well-known proposal for an axiomatic characterization of infinitesimal objects in a 1-topos goes by the name synthetic differential geometry, where infinitesimal extension is characterized by algebraic properties of dual function algebras, as above. From the point of view and in the presence of cohesion in an ∞-topos, however, there is a more immediate geometric characterization (dcct)
I’m reviewing the book for MathSciNet, it would be good to discuss some of the less familiar concepts and record them on the lab.
That would be helpful. Is the field sufficiently identified with Bunge that you could record these on synthetic differential topology, or should there be a special page for the book?
added pointer to Penon’s thesis and to logical topology.
1 to 5 of 5