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### Session S27 - Categories and Topology

Thursday, July 15, 13:30 ~ 14:00 UTC-3

My thesis introduced restriction monads in bicategories containing a suitable 0-cell $E$ and a restriction operator defined by a family of functions indexed by so-called $E$-elemental 1-cells. In $\mathrm{Span}(\mathbf{Set})$, this suitably-defined $E$ works out to be a single-element set, or a terminal object in $\mathbf{Set}$. This talk extends this notion to generalized objects to include bicategories without enough elements. We will then give examples and applications.