Category Of Grey Sets

Msoomeh Hezarjaribi\(^{a,∗}\), Davood Darvishi Solokolaei \(^b\), Zohreh Habibi\(^c\)

\(^a\)Department of Mathematics, Payame Noor University(PNU),Tehran, Iran.

\(^b\)Department of Mathematics, Payame Noor University(PNU),Tehran, Iran.
\(^c\)Department of Mathematics, Payame Noor University(PNU),Tehran, Iran.

Correspondence should be addressed to: Msoomeh.hezarjaribi@pnu.ac.ir, d−darvishi@pnu.ac.ir, Z−habibi@pnu.ac.ir

Copyright © 2024 Msoomeh Hezarjaribi, Davood Darvishi Solokolaei, Zohreh Habibi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 03 June 2022 Accepted: 22 August 2024; Published Online: 29 August 2024

Abstract

In this paper, we introduce the concept of morphisms between two grey sets and defined a new category, namely, GSet, of grey sets and grey morphisms. We investigate some categorical notions such product, coproduct, pullback, and pushout. Additionally, we study equalizer and coequalizer for pairs of grey morphisms and show that any grey set has an injective hull.

Keywords:

Coincidence point, category, grey morphism, grey set.