structures in a cohesive (∞,1)-topos
infinitesimal cohesion?
typical contexts
A context of differential cohesion is determined by the existence of an adjoint triple of modalities
where $\Re$ and $\&$ are idempotent comonads and $\Im$ is an idempotent monad. Here $\Im$ is called the infinitesimal shape modality.
An object/type $X$ is called formally smooth if the unit
is a 1-epimorphism. This is equivalent to the essentially unique morphism $X \to *$ to the terminal object being a formally smooth morphism.
(shape modality $\dashv$ flat modality $\dashv$ sharp modality)
$(ʃ \dashv \flat \dashv \sharp )$
dR-shape modality$\dashv$ dR-flat modality
$ʃ_{dR} \dashv \flat_{dR}$
(reduction modality $\dashv$ infinitesimal shape modality $\dashv$ infinitesimal flat modality)
$(\Re \dashv \Im \dashv \&)$
fermionic modality$\dashv$ bosonic modality $\dashv$ rheonomy modality
$(\rightrightarrows \dashv \rightsquigarrow \dashv Rh)$
Last revised on August 24, 2018 at 08:13:03. See the history of this page for a list of all contributions to it.