Identify the correct fully-extended source and target categories

Determine the appropriate 2-category of super Euclidean bordisms and the appropriate 3-category that deloops the 2-category of Z/2-graded algebras and bimodules to define fully-extended field theories satisfying excision in the Stolz–Teichner framework.

Background

Excision and fully-extended field theories require lifting the 1-categorical bordism description to higher categories: a 2-category of super Euclidean bordisms and a 3-category deloop of the target 2-category. Multiple generalizations exist.

The authors note that neither source nor target are uniquely determined by the current definitions, and it is presently unclear which choices correctly capture the intended geometry and analysis for proving the conjectures.