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An anti-reduced object or simple infinitesimal type is one whose reduction is the point, hence one consisting entirely of “infinitesimal extension”, i.e. an infinitesimally thickened point.
In the context of differential cohesion, an anti-reduced obect is an comodal type $X$ for the infinitesimal shape modality $\Im$
In homotopy type theory/higher topos theory anti-reduced types are essentially what is also called “formal moduli problems” (these are typically required to satisfy one more condition besides being anti-reduced, namely being infinitesimally cohesive in the sense of Lurie).
(shape modality $\dashv$ flat modality $\dashv$ sharp modality)
$(\esh \dashv \flat \dashv \sharp )$
dR-shape modality$\dashv$ dR-flat modality
$\esh_{dR} \dashv \flat_{dR}$
(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 March 5, 2015 at 17:47:46. See the history of this page for a list of all contributions to it.