Publication Date
9-11-1967
Abstract
Croisot [1] was apparently first to examine some of the properties of residuated mappings. It is the purpose of this paper to show that certain constructions currently useful in homological algebra can be made in a suitable category of partially ordered sets with residuated mappings. In Section 1 we note some elementary properties of residuated mappings all of which are well known cf. Janowitz [4]. In Section 2 we notice some properties of various categories of partially ordered sets with residuated mappings. In Section 3 we prove that the category of complete lattices with residuated mappings has enough injectives and projectives and we obtain a characterization of these. In Section 4 we prove that has enough limits and colimits. In Section 5 we define the functors (-, M) and (M, -) and we observe that (M,-) preserves limits while (-,M) carries colimits to limits. In Section 6 we define exact sequences in and we observe that (M,-) and (-, M) are left-exact functors. The following is a list of basic definitions. If the reader is familiar with Mitchell [5] he may proceed to Section 1.
Degree Name
Mathematics
Level of Degree
Doctoral
Department Name
Mathematics & Statistics
First Committee Member (Chair)
Richard Clyde Metzler
Second Committee Member
Julius Rubin Blum
Third Committee Member
Lambert Herman Koopmans
Language
English
Document Type
Dissertation
Recommended Citation
Crown, Gary D.. "On Some Categories of Partially Ordered Sets with Residuated Mappings." (1967). https://digitalrepository.unm.edu/math_etds/241