6533b850fe1ef96bd12a82d8
RESEARCH PRODUCT
On limits and colimits of variety-based topological systems
Sergey A. Solovyovsubject
Limit (category theory)Artificial IntelligenceLogicMathematics::Category TheoryConcrete categoryCategory of topological spacesVariety (universal algebra)Algebraic topologySpace (mathematics)TopologyCategory of setsReflective subcategoryMathematicsdescription
The paper provides variety-based extensions of the concepts of (lattice-valued) interchange system and space, introduced by Denniston, Melton and Rodabaugh, and shows that variety-based interchange systems incorporate topological systems of Vickers, state property systems of Aerts, Chu spaces (over the category of sets in the sense of Pratt) of P.-H. Chu and contexts (of formal concept analysis) of Wille. The paper also provides an explicit description of (co)limits in the category of variety-based topological systems and applies the obtained results to extend the claim of Denniston et al. that the category of topological systems of Vickers is small initially topological over the category of sets.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-01 | Fuzzy Sets and Systems |