We give a purely category-theoretic proof of the result of Makkai and Paré saying that the category Lin of linearly ordered sets and order preserving injective mappings is a minimal finitely accessible category. We also discuss the existence of a minimal ℵ_1-accessible category.
Keywords: accessible category, indiscernibles, linear order
2020 MSC: 18C35, 03C48
Theory and Applications of Categories, Vol. 36, 2021, No. 10, pp 280-287.