Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T16:33:50.786Z Has data issue: false hasContentIssue false
  • English
  • Français

An Epi-Reflector for Universal Theories

Published online by Cambridge University Press:  20 November 2018

Paul D. Bacsich
Paul D. Bacsich*
Affiliation:
Open University, Bletchley, Buckinghamshire U.K.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A construction of an epi-reflector by injective hull techniques is given which applies to the class of models of any universal theory with the Amalgamation Property and there yields a weak but functorial type of algebraic closure. Various completions such as the boolean envelope and quotient field constructions are identified as such injective hulls over epimorphic injections. Forms of the Amalgamation Property are also shown to eliminate various pathologies of epimorphisms and equalizers.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 167 - 171
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Banaschewski, B., Injectivity and essential extensions in equational classes of algebras, Proceedings of the Queen’s University Conference on Universal Algebra (1969), Queen’s papers No. 25, 1970.Google Scholar
2. Banaschewski, B. and Bruns, G., Injective hulls in the category of distributive lattices, Crelle’s J. 232 (1968), 102–109.Google Scholar
3. Garling, D., Some remarks on injective envelopes, Proc. Amer. Math. Soc. 27 (1971), 503–505.Google Scholar
4. Isbell, J., Epimorphisms and dominions, Proceedings of the Conference on Categorical Algebra, La Jolla 1965, Springer-Verlag, Berlin, 1967.Google Scholar
5. Jόnsson, B., Algebraic extensions of relational systems, Math. Scand. 11 (1962), 179–205.Google Scholar
6. Kelly, G., Monomorphisms, epimorphisms, and pullbacks, J. Austral. Math. Soc. 9 (1969), 124–142.Google Scholar
7. Kennison, J., Full reflective subcategories and generalised covering spaces, Illinois J. Math. 12 (1968), 353–365.Google Scholar
8. Semadeni, Z., Projectivity, injectivity, and duality, Rozprawy Matematyczne 35, 1963.Google Scholar
9. Stone, M., Topological representation of distributive lattices and Brouwerian logics, Časopis Pěst. Mat. 67 (1937), 1–25.Google Scholar