Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-15T12:54:39.748Z Has data issue: false hasContentIssue false
  • English
  • Français

Homomorphisms of (0, 1)-lattices with a given sublattice and quotient

Published online by Cambridge University Press:  18 May 2009

Václav Koubek
Václav Koubek
Affiliation:
Faculty of Mathematical Physics, Malostraské NÁM 25, 11800 Praha 1, Czechoslovakia
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.

Let us recall the notions of full embedding and universality of categories we will be using throughout.

A full embedding is a functor F taking the objects of a source category A injectively to objects of a target category B and the hom-sets HomA(a, b) bijectively to the hom-sets HomR(F(a), F(b)). If A is a subcategory of B and the corresponding inclusion functor is a full embedding then A is said to be a full subcategory of B. In this case we have HomA(a, b) = HomB(a, b) for any a, b in A; that is to say, a full subcategory is completely determined, within a given category, by specifying the class of its objects. A category U is termed universal if an arbitrary category of algebras can be fully embedded in U.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 159 - 170
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Adams, M. E. and Sichler, J., Homomorphisms of bounded lattices with a given sublattice, Arch. Math. Basel 30 (1978), 122–128.CrossRefGoogle Scholar
2.Adams, M. E. and Sichler, J., Cover set lattices, Canad. J. Math. 32 (1980), 1177–1205.Google Scholar
3.Crawley, P. and Dilworth, R. P., Algebraic theory of lattices (Prentice-Hall, 1973).Google Scholar
4.Dean, R. A., Free lattices generated by partially ordered sets and preserving bounds, Canad. J. Math. 16 (1964), 136–148.CrossRefGoogle Scholar
5.Goralčik, P., Koubek, V. and Sichler, J., Universal varieties of (0, l)-lattices, Canad. J. Math. 42 (1990), 470–490.Google Scholar
6.Grätzer, G., General lattice theory (Academic Press, 1978).Google Scholar
7.Grätzer, G. and Sichler, J., On the endomorphism semigroup (and category) of bounded lattices, Pacific J. Math. 35 (1970), 639–647.Google Scholar
8.Hedrlin, Z. and Sichler, J., Any boundable binding category contains a proper class of mutually disjoint copies of itself, Algebra Universalis 1 (1971), 97–103.Google Scholar
9.Koubek, V., Graphs with given subgraphs represent all categories, Comment. Math. Univ. Carolin. 18 (1977), 115–127.Google Scholar
10.Koubek, V., Graphs with given subgraphs represent all categories II, Comment. Math. Univ. Carolin. 19 (1978), 249–263.Google Scholar
11.Koubek, V., Towards minimal binding varieties of lattices, Canad. J. Math. 36 (1984), 263–285.Google Scholar
12.Koubek, V. and Sichler, J., Universality of small lattice varieties, Proc. Amer. Math. Soc. 91 (1984), 19–24.CrossRefGoogle Scholar
13.Koubek, V. and Sichler, J., Quotients of rigid (0, l)-lattices, Arch. Math. Basel 44 (1985), 403–412.CrossRefGoogle Scholar
14.Lakser, H., Normal and canonical representations in free products of lattices, Canad. J. Math. 22 (1970), 394–402.Google Scholar
15.Pultr, A. and Trnková, V., Combinatorial, algebraic and topological representations of groups, semigroups and categories (North Holland, 1980).Google Scholar
16.Taylor, W., Review of seventeen papers on equational compactness, J. Symbolic Logic 40 (1975), 88–92.Google Scholar