A Categorical Approach to Rough Equality Algebras via Approximation Functors
A Categorical Approach to Rough Equality Algebras via Approximation Functors
This paper develops a categorical framework for congruence-based rough set theory on equality algebras. We introduce the category AppEqAlg of equality algebras equipped with a congruence, analyse the induced rough upper and lower approximations on the power set and on the lattice of subalgebras, and characterise exact (θ-definable) subalgebras via the quotient algebra E/θ. On the categorical side we construct the quotient functor U : AppEqAlg → EqAlg and the diagonal embedding G : EqAlg → AppEqAlg, prove the adjunction U ⊣ G, and show that the forgetful functor V : AppEqAlg → EqAlg is topological, so that (co)limits lift from EqAlg with canonical congruences.
Equality algebras, Rough set theory, Rough algebraic structures, Topological concrete categories, Congruence lattices, Algebraic logic, Category theory, Closure and interior operators
Equality algebras, Rough set theory, Rough algebraic structures, Topological concrete categories, Congruence lattices, Algebraic logic, Category theory, Closure and interior operators
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