Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T11:45:26.193Z Has data issue: false hasContentIssue false
  • English
  • Français

Testing Categories and Strong Universality

Published online by Cambridge University Press:  20 November 2018

J. Sichler
J. Sichler*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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 category A is binding (or universal) if any full category of algebras is isomorphic to a full subcategory of A. There are many binding categories: the category of all commutative rings with unit and all unit-preserving homomorphisms [1], the category of bounded lattices [2], the category of semigroups [3], the category A(1, 1) of all algebras with two unary fundamental operations and the category of directed graphs [4], the category of all commutative groupoids [11] and many others.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 370 - 385
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Fried, E. and Sichler, J., Homomorphisms of commutative rings with unit element (to appear).Google Scholar
2. Grätzer, G. and Sichler, J., On the endomorphism semigroup (and category) of bounded lattices, Pacific J. Math. 35 (1970), 639–647.Google Scholar
3. Hedrlin, Z. and Lambek, J., How comprehensive is the category of semigroups, J. Algebra 11 (1969), 195–212.Google Scholar
4. Hedrlin, Z. and Pultr, A., On full embeddings of categories of algebras, Illinois J. Math. 10 (1966), 392–406.Google Scholar
5. Hedrlin, Z. and Pultr, A., Relations (graphs) with given infinite semigroups, Monatsh. Math. 68 (1964), 421–425.Google Scholar
6. 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
7. Isbell, J. R., Algebras of uniformly continuous functions, Ann. of Math. 68 (1958), 96–125.Google Scholar
8. Pultr, A., Eine Bemerkung ilber voile Einbettungen von Kategorien von Algebren, Math. Ann. 178 (1968), 78–82.Google Scholar
9. Pultr, A., On full embeddings of concrete categories with respect to forgetful functors, Comment. Math. Univ. Carolinae 9 (1968), 281–304.Google Scholar
10. Sichler, J., . 4(1, 1) can be strongly embedded into the category of semigroups, Comment. Math. Univ. Carolinae 9 (1968), 257–262.Google Scholar
11. Sichler, J., The category of commutative groupoids is binding, Comment. Math. Univ. Carolinae 8 (1967), 753–755.Google Scholar
12. Sichler, J., Concerning minimal primitive classes of algebras containing any category of algebras as a full subcategory, Comment. Math. Univ. Carolinae 9 (1968), 627–635.Google Scholar
13. Trnková, V., Strong embedding of category of all groupoids into category of semigroups. Comment. Math. Univ. Carolinae 9 (1968), 251–256.Google Scholar
14. Vopěnka, P., Pultr, A., and Hedrlin, Z., A rigid relation exists on any set, Comment. Math. Univ. Carolinae 6 (1965), 149–155.Google Scholar