Dice Question Streamline Icon: https://streamlinehq.com

Formulate codereliction axioms purely within monoidal category theory

Determine whether the axioms defining a codereliction transformation can be expressed entirely using the standard structures and concepts of monoidal category theory, without introducing additional ad hoc invertible 2-cells or extra coherence data. This would provide a formulation of codereliction that does not rely on auxiliary diagrams beyond monoidal categorical primitives.

Information Square Streamline Icon: https://streamlinehq.com

Background

The paper develops a bicategorical counterpart of codereliction to model differential linear logic. While the authors provide a workable two-dimensional definition using canonical 2-cells, they note conceptual difficulties in expressing codereliction purely in terms of monoidal categorical primitives. This issue affects coherence and the formulation of axioms.

A resolution would clarify whether codereliction can be axiomatized in the one-dimensional monoidal setting without recourse to additional structure, thereby informing both the classical theory of differential categories and its bicategorical generalizations.

References

The definition of a codereliction presented additional problems, in that it is not known whether its axioms can be expressed purely in terms of the basic concepts of the theory of monoidal categories. For this reason, if we were to require the presence of invertible 2-cells in the diagrams that are part of the definition of a codereliction transformation in [BluteR:difcr], we would then be facing the question of what coherence axioms to impose on them, which appears to be a difficult question.

— Monoidal bicategories, differential linear logic, and analytic functors (2405.05774 - Fiore et al., 9 May 2024) in Introduction, Technical aspects