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On orthogonal subcategories of locally presentable categories. (English) Zbl 0767.18002

The authors prove that the statement “every full limit-closed subcategory of a locally presentable category is orthogonal” is undecidable. It is equivalent to a large-cardinal principle. For dual categories of locally presentable categories the situation is analogous.

MSC:

18A35 Categories admitting limits (complete categories), functors preserving limits, completions
03E55 Large cardinals
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References:

[1] Adámek, J.; Rosický, J.; Trnková, V., Are all limit-closed subcategories of locally presentable categories reflective?, (Categorical Algebra and Applications. Categorical Algebra and Applications, Lecture Notes in Math., Vol. 1348 (1988), Springer: Springer Berlin), 1-18 · Zbl 1329.18003
[2] Jech, T., Set Theory (1978), Academic Press: Academic Press New York · Zbl 0419.03028
[3] Pultr, A.; Trnková, V., Combinatorial, Algebraic and Topological Representations of Groups, (Semigroups and Catergories (1980), North-Holland: North-Holland Amsterdam) · Zbl 0418.18004
[4] Rosický, J.; Trnková, V.; Adámek, J., Unexpected properties of locally presentable categories, Algebra Universalis, 27, 153-170 (1990) · Zbl 0701.18003
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