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is often assumed for the definition of "posetal"; in the case of a category that is posetal, being skeletal is equivalent to the requirement that the only isomorphisms are the identity morphisms, equivalently that the preordered class satisfies
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structures are definable as posetal categories of a certain kind, usually with the stronger assumption of being skeletal. For example, under this assumption, a poset may be defined as a small posetal category, a
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each contain at most one morphism. As such, a posetal category amounts to a
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of posets, distributive lattices, Heyting algebras, and
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