TY - UNPB
T1 - Free Doubly-Infinitary Distributive Categories are Cartesian Closed
AU - Nunes, Fernando Lucatelli
AU - Vákár, Matthijs
PY - 2024/3/15
Y1 - 2024/3/15
N2 - 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.
AB - 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.
U2 - 10.48550/ARXIV.2403.10447
DO - 10.48550/ARXIV.2403.10447
M3 - Preprint
SP - 1
EP - 16
BT - Free Doubly-Infinitary Distributive Categories are Cartesian Closed
PB - arXiv
ER -