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higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
A sheaf topos is called strongly stably locally connected if it is a locally connected topos
such that the extra left adjoint in addition preserves finite products (the terminal object and binary products).
This means it is in particular also a connected topos.
If preserves even all finite limits then is called a totally connected topos.
If a strongly stably locally connected topos is also alocal topos, then it is a cohesive topos.
The “strong” in “strongly connected” may be read as referring to being a strong adjunction in that we have a natural isomorphism for the internal homs in the sense that
This follows already for connected and essential if preserves products, because this already implies the equivalent Frobenius reciprocity isomorphism. See here for more.
locally connected topos / locally ∞-connected (∞,1)-topos
strongly stably locally connected topos / strongly ∞-connected (∞,1)-topos
and
Last revised on December 18, 2022 at 16:59:08. See the history of this page for a list of all contributions to it.