关于光学、透镜与Dialectica范畴的纤维化构造
范畴论
2024-12-18 v5 信息论
计算机科学中的逻辑
math.IT
摘要
透镜/光学范畴与Dialectica范畴均由基本形式相同的双向态射构成。在这项工作中，我们展示了它们如何被视为一个总括性纤维化构造的特例，该构造推广了Hofstra的Dialectica纤维化构造和Spivak的广义透镜构造。此构造通过使用对偶纤维化构造迭代地扭转每个分量，将一个Grothendieck纤维化塔转化为另一个纤维化塔。
引用
@article{arxiv.2403.16388,
title = {On a fibrational construction for optics, lenses, and Dialectica categories},
author = {Matteo Capucci and Bruno Gavranović and Abdullah Malik and Francisco Rios and Jonathan Weinberger},
journal= {arXiv preprint arXiv:2403.16388},
year = {2024}
}
备注
v3: 18 pp. Project results from the American Mathematical Society's Math Research Community on Applied Category Theory 2022. v4: Final version for proceedings of MFPS 2024. Updated author affiliation. v5: Corrected author typo, added MPIM report no and DOI