Year: 2026
Type: article
Abstract: Working in an arbitrary category endowed with a fixed $$(\mathcal {E}, \mathcal {M})$$ -factorization system in which the preimage functor for any given morphism preserves arbitrary joins we improve the Castellini notion of hereditary interior operators. We introduce and study a general notion of hereditary interior operators in terms of dual images. It is shown that these operators behave as well as hereditary closure operators. In particular, hereditary interior operators are characterized in terms of the notion of initiality as for hereditary closure operators. Moreover, we prove that additive hereditary interior operators are Castellini’s hereditary interior operators. Some examples are included.
Source: Afrika Matematika
Authors: Fikreyohans Solomon Assfaw, David Holgate
Institution: University of the Western Cape
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Funder: University of the Western Cape
OpenAlex ID: W7129019104