# On the Categories of Coalgebras, Dialgebras and Powerset Theory over L-Fuzzy Approximation Spaces

### Sutapa Mahato, S. Tiwari

#### 2023

#### Abstract

This paper is to establish a relationship between powerset theories and the category of dialgebras over the category of L-fuzzy approximation space, where L is a residuated lattice. Also, we show that the category FAS of L-fuzzy approximation spaces is a category of F-coalgebras. Interestingly, we introduce a functor having both the left/right adjoint from the category FAS to the category UAS of upper approximation sets. Further, the category J-Coal of J-coalgebras and the category (J,K)-Dial of (J;K)-dialgebras are introduced over the category FAS and it is shown that they are topological categories.

Download#### Paper Citation

#### in Harvard Style

Mahato S. and Tiwari S. (2023). **On the Categories of Coalgebras, Dialgebras and Powerset Theory over L-Fuzzy Approximation Spaces**. In *Proceedings of the 15th International Joint Conference on Computational Intelligence - Volume 1: FCTA*; ISBN 978-989-758-674-3, SciTePress, pages 348-358. DOI: 10.5220/0012182100003595

#### in Bibtex Style

@conference{fcta23,

author={Sutapa Mahato and S. Tiwari},

title={On the Categories of Coalgebras, Dialgebras and Powerset Theory over L-Fuzzy Approximation Spaces},

booktitle={Proceedings of the 15th International Joint Conference on Computational Intelligence - Volume 1: FCTA},

year={2023},

pages={348-358},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012182100003595},

isbn={978-989-758-674-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Computational Intelligence - Volume 1: FCTA

TI - On the Categories of Coalgebras, Dialgebras and Powerset Theory over L-Fuzzy Approximation Spaces

SN - 978-989-758-674-3

AU - Mahato S.

AU - Tiwari S.

PY - 2023

SP - 348

EP - 358

DO - 10.5220/0012182100003595

PB - SciTePress