Free Doubly-Infinitary Distributive Categories are Cartesian Closed
<|reference_start|>Free Doubly-Infinitary Distributive Categories are Cartesian Closed: We delve into the concept of categories with products that distribute over coproducts, which we call doubly-infinitary distributive categories. We show various instances of doubly-infinitary distributive categories aiming for a comparative analysis with established notions such as extensivity, infinitary distributiveness, and cartesian closedness. Our exploration reveals that this condition represents a substantial extension beyond the classical understanding of infinitary distributive categories. Our main theorem establishes that free doubly-infinitary distributive categories are cartesian closed. We end the paper with remarks on non-canonical isomorphisms, open questions, and future work.<|reference_end|>
@article{nunes2024free,
    title={Free Doubly-Infinitary Distributive Categories are Cartesian Closed},
    author={Fernando Lucatelli Nunes and Matthijs V'ak'ar},
    journal={arXiv preprint arXiv:2403.10447},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.10447},
    primaryClass={math.CT cs.LO cs.PL math.LO}
}