Stellenbosch University
Interior operators and the category of
(pre)sheaves
Fikreyohans Solomon Assfaw, University
of the Western Cape
SAMS Subject Classification Number: 4
Motivated by the theory of categorical closure operators, the categorical notion of interior operators was introduced by [3]. These operators have received more recent attention and a few papers are published on the subject (see [1]). Working in an arbitrary category in which each pullback functor commutes with the join of subobjects, we further study interior operators. In particular, we define and investigate interior operators on the category of pre(sheaves). Furthermore, we examine the notions of heredity, openness, closedness, initiality, and finality with respect to the defined interior operators.
References
[1] F. S. Assfaw and D. Holgate, Codenseness and openness with respect to an interior operator, Appl. Categ. Structures. 29(2) (2021), 235–248.
[2] S. Mac Lane and I. Moerdijk, A first introduction to topos theory, Springer-Verlag, 1992.
[3] Vorster, S., Interior operators in general categories, Quaest. Math. 23(4) (2000), 405–416.
