## Anthony W. Hager, Brian Wynne

*The category of compactifications and its coreflections*

Comment.Math.Univ.Carolin. 63,3 (2022) 365-378.**Abstract: **We define ``the category of compactifications", which is denoted {\bf{CM}}, and consider its family of coreflections, denoted {\bf{corCM}}. We show that {\bf{corCM}} is a complete lattice with bottom the identity and top an interpretation of the Čech-Stone \beta. A c \in{\bf{corCM}} implies the assignment to each locally compact, noncompact Y a compactification minimum for membership in the ``object-range" of c. We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms in {\bf{corCM}} (thus {\bf{corCM}} is not a set), show that any c \in{\bf{corCM}} not the identity is above an atom, and that \beta is not the supremum of atoms.

**Keywords:** compactification; coreflection; atom in a lattice

**DOI:** DOI 10.14712/1213-7243.2022.024

**AMS Subject Classification:** 54B30 54C10 54D35 06B23 18A40

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