Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-22T08:50:20.729Z Has data issue: false hasContentIssue false
  • English
  • Français

Injective hulls as completions

Published online by Cambridge University Press:  18 May 2009

Paul D. Bacsich
Paul D. Bacsich
Affiliation:
Mathematical Institute, Oxford University
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 preliminary attempt is made to place the theory of completions of boolean algebras and of partially ordered sets in a wider context. The theory and construction of injective hulls in abelian categories is generalised and it is demonstrated that any variety with enough injectives admits injective hulls. Then the methods developed are applied to a non-algebraic bicategory, that of ordered sets.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 1 , March 1972 , pp. 17 - 23
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Bacsich, P., Algebraic injectivity and weak choice axioms, Ph.D. Thesis, University of Bristol, 1970.Google Scholar
2.Balbes, R., Projective and injective distributive lattices, Pacific J. Math. 21 (1967), 405–420.CrossRefGoogle Scholar
3.Banaschewski, B. and Bruns, G., Categorical characterisation of the MacNeille completion, Arch. Math. Basel 18 (1967), 369–377.Google Scholar
4.Birkhoff, G., Lattice theory, Amer. Math. Soc. Colloquium Publications 25 (Providence, R.I., 1967).Google Scholar
5.Bruns, G. and Lakser, H., Injective hulls of semilattices, Canad. Math. Bull. 13 (1970), 115–118.Google Scholar
6.Cohen, H., Injective envelopes of Banach spaces, Bull. Amer. Math. Soc. 70 (1964), 723–726.Google Scholar
7.Cohn, P., Universal algebra (New York, 1965).Google Scholar
8.Daigneault, A., Injective envelopes, Amer. Math. Monthly 76 (1969), 766–774.Google Scholar
9.Freyd, P., Abelian categories (New York, 1964).Google Scholar
10.Gleason, A., Projective topological spaces, Illinois J. Math. 2 (1958), 482–489.CrossRefGoogle Scholar
11.Halmos, P., Lectures on Boolean algebras (Princeton, 1963).Google Scholar
12.Isbell, J., Algebras of uniformly continuous functions, Ann. of Math. 68 (1958), 96–125.Google Scholar
13.McCoy, N. and Montgomery, D., A representation of generalised Boolean rings, Duke Math. J. 3 (1937), 455–459.CrossRefGoogle Scholar
14.Mitchell, B., Theory of categories (New York, 1965).Google Scholar
15.Scott, D., Lectures on Boolean-valued models for set theory, Summer Institute in Set Theory, Los Angeles, 1967 (to appear).Google Scholar
16.Semadeni, Z., Projectivity, injectivity and duality, Rozprawy Matematyczne 35 (1963).Google Scholar
17.Sikorski, R., A theorem on extension of homomorphisms, Ann. Soc. Pol. Math. 21 (1948), 332–335.Google Scholar
18.Sikorski, R., Boolean algebras, 2nd edn (Berlin, 1964).Google Scholar