I am interested in category theory and its applications in topology, algebra and computer science.


  • J. He, H. Lai and L. Shen. Towards probabilistic partial metric spaces: Diagonals between distance distributions. arXiv:1801.05966, 2018. [Preprint] [arXiv]
  • C.-Y. Du, L. Shen and X. Zhao. Spark complexes on good effective orbifold atlases categorically. arXiv:1708.07551, 2017. [Preprint] [arXiv]
  • J. Gutiérrez García, H. Lai and L. Shen. Fuzzy Galois connections on fuzzy sets. arXiv:1707.08849, 2017. [Preprint] [arXiv]
  • H. Lai and L. Shen. Regularity vs. constructive complete (co)distributivity. arXiv:1606.08930, 2016. [Preprint] [arXiv]


  1. H. Lai, L. Shen and W. Tholen. Lax distributive laws for topology, II. Theory and Applications of Categories, 32(21):736-768, 2017. [Preprint] [arXiv] [Journal]
  2. H. Lai and L. Shen. Fixed points of adjoint functors enriched in a quantaloid. Fuzzy Sets and Systems, 321:1-28, 2017. [Preprint] [arXiv] [Journal]
  3. L. Shen. Q-closure spaces. Fuzzy Sets and Systems, 300:102-133, 2016. [Preprint] [arXiv] [Journal]
  4. L. Shen, Y. Tao and D. Zhang. Chu connections and back diagonals between Q-distributors. Journal of Pure and Applied Algebra, 220(5):1858-1901, 2016. [Preprint] [arXiv] [Journal]
  5. L. Shen and W. Tholen. Topological categories, quantaloids and Isbell adjunctions. Topology and its Applications, 200:212-236, 2016. [Preprint] [arXiv] [Journal]
  6. L. Shen and W. Tholen. Limits and colimits of quantaloid-enriched categories and their distributors. Cahiers de Topologie et Géométrie Différentielle Catégoriques, 56(3):209-231, 2015. [Preprint] [arXiv] [Journal]
  7. L. Shen and D. Zhang. Categories enriched over a quantaloid: Isbell adjunctions and Kan adjunctions. Theory and Applications of Categories, 28(20):577-615, 2013. [Preprint] [arXiv] [Journal]
  8. L. Shen and D. Zhang. Formal concept analysis on fuzzy sets. Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, 215-219. [Preprint] [Journal]
  9. L. Shen and D. Zhang. The concept lattice functors. International Journal of Approximate Reasoning, 54(1):166-183, 2013. [Preprint] [Journal]
  10. L. Shen and D. Zhang. Many-valued state property systems and closure spaces. Journal of Sichuan University (Natural Science Edition), 49(4):735-739, 2012. [Preprint] [Journal]


  • L. Shen. Adjunctions in Quantaloid-enriched Categories. PhD thesis, Sichuan University, Chengdu, 2014. [English Version] [arXiv] [Chinese Version]
  • L. Shen. Functorial Properties of Concept Lattices. Master thesis, Sichuan University, Chengdu, 2011. [Chinese Version]


  • The theory of many-valued topology based on lax algebras, 2018.1 - 2020.12, RMB 250K. A Young Scientists Fund from National Natural Science Foundation of China (No. 11701396).
  • The theory of Q-categories and its applications, 2016.6 - 2019.6, RMB 150K. A startup grant from Sichuan University (No. YJ201644).