# Linear Exponential Comonads without Symmetry

## TL;DR

This paper extends the concept of linear exponential comonads from symmetric to general monoidal categories, broadening the theoretical framework for modeling exponential modalities in linear logic.

## Contribution

It introduces linear exponential comonads on non-symmetric monoidal categories and establishes foundational results for their properties.

## Key findings

- Extended linear exponential comonads to non-symmetric monoidal categories
- Established basic properties of these comonads
- Broadened the theoretical framework for linear logic modeling

## Abstract

The notion of linear exponential comonads on symmetric monoidal categories has been used for modelling the exponential modality of linear logic. In this paper we introduce linear exponential comonads on general (possibly non-symmetric) monoidal categories, and show some basic results on them.