Cartesian closedness in categories with an idempotent closure operator and closed morphisms
| Autor: | Josef Šlapal |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics Monotonic function 010103 numerical & computational mathematics 01 natural sciences law.invention Cartesian closed category Morphism law Mathematics::Category Theory Lattice (order) Idempotence Subobject Discrete Mathematics and Combinatorics Closure operator Cartesian coordinate system 0101 mathematics Mathematics |
| Zdroj: | Aequationes mathematicae. 96:129-136 |
| ISSN: | 1420-8903 0001-9054 |
| DOI: | 10.1007/s00010-020-00772-9 |
| Popis: | Given a subobject-structured category $$\mathcal X$$ , we construct a new category whose objects are the pairs (X, c) where X is an $$\mathcal X$$ -object and c is an idempotent, monotonic and extensive endomap of the subobject lattice of X, and whose morphisms between objects are the closed maps between the corresponding subobject lattices. We give a sufficient condition on $$\mathcal X$$ for the new category to be cartesian closed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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