We show that the category of partially ordered sets Pos is the free conservative cocompletion of the category of finite non-empty totally ordered sets Δ, also known as the simplex category. This means that Pos is the initial cocomplete category that contains Δ as a full subcategory and preserves the existing colimits of Δ.
Keywords: cocompletion, partial orders, simplex category
2020 MSC: 18A35
Theory and Applications of Categories, Vol. 44, 2025, No. 1, pp 1-14.
Published 2025-01-05.
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