= Capital regular category
A capital regular category, in the convention of https://www2.math.ethz.ch/EMIS/journals/TAC/volumes/16/31/16-31.pdf[Definitions 1.1–1.3], is a <regular category> whose <well-supported objects> are <well-pointed objects in a category>. It does not require arbitrary objects to be detected by global points. A <partially ordered set> with finite meets, regarded as a <category>, is capital: its only well-supported object is the top element. Such a category can have many proper subterminal objects, all with no points. This example distinguishes the definition from the stronger convention that the global-sections functor reflects every isomorphism.
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