Relative field theories via relative dualizability

Abstract We investigate relative versions of dualizability designed for relative versions of topological field theories (TFTs), also called twisted TFTs, or quiche TFTs in the context of symmetries. In even dimensions, we show an equivalence between lax and oplax fully extended framed relative topological field theories valued in an $$(\infty , N)\text {-}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo>)</mml:mo> <mml:mtext>-</mml:mtext> </mml:mrow> </mml:math> category in terms of adjunctibility. Motivated by this, we systematically investigate higher adjunctibility conditions and their implications for relative TFTs. Our analysis leads us to identify the oplax relative TFT as the notion of choice. Finally, for fun we explore a tree version of adjunctibility and compute the number of equivalence classes thereof.