Geodesic
Partial orders are the free conservative cocompletion of total orders
Theory and applications of categories, Tome 44 (2025), pp. 1-14

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Publié le :
Classification : 18A35
Keywords: cocompletion, partial orders, simplex category 
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     author = {Calin Tataru},
     title = {Partial orders are the free conservative cocompletion of total orders},
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     publisher = {mathdoc},
     volume = {44},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2025_44_a0/}
}
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Calin Tataru. Partial orders are the free conservative cocompletion of total orders. Theory and applications of categories, Tome 44 (2025), pp. 1-14. http://geodesic.mathdoc.fr/item/TAC_2025_44_a0/