Isbell, John Locally finite adequate subcategories. (English) Zbl 0555.18001 J. Pure Appl. Algebra 36, 219-220 (1985). It is shown that a complete category which is not preordered cannot have a two-sided adequate subcategory all of whose hom-sets are finite. The proof involves compact Hausdorff topologies. A stronger result is obtained in this work by decomposing adequacy. Reviewer: P.L.Ferrari MSC: 18A35 Categories admitting limits (complete categories), functors preserving limits, completions 18B35 Preorders, orders, domains and lattices (viewed as categories) 54D45 Local compactness, \(\sigma\)-compactness Keywords:preordered category; finite hom-sets; complete category; adequate subcategory; compact Hausdorff topologies; decomposing adequacy × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Isbell, J., Uniform neighborhood retracts, Pacific J. Math., 11, 609-648 (1961) · Zbl 0109.15402 [2] Isbell, J., Subobjects, adequacy, completeness and categories of algebras, Rozprawy Mat., 36 (1964) · Zbl 0133.26703 [3] Isbell, J., Small adequate subcategories, J. London Math. Soc., 43, 242-246 (1968) · Zbl 0155.03601 [4] MacLane, S., Categories for the Working Mathematician (1971), Springer: Springer New York · Zbl 0232.18001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.