In Hasegawa's paper “On Traced Monoidal Closed Categories”, he showed that a traced monoidal category was closed if and only if the canonical functor into the its INT construction has a right adjoint. As a consequence, every traced monoidal closed category is a reflexive subcategory of a compact closed category. As such, for a traced monoidal closed category, there is an idempotent comonad on its INT construction. Hasegawa pondered an open question of if there was a possible adjunction between traced monoidal closed categories and compact closed categories with a suitable notion of idempotent comonad. In this talk, I will review the main results of Hasegawa's paper and answer his open question (hopefully correctly!).