The main purpose of this paper is to show that the converse of the known implication weakly action representable implies action accessible is false. In particular we show that both action accessibility, as well as the (at least formally stronger) condition requiring the existence of all normalizers do not imply weakly-action-representability even for varieties. In addition we show that in contrast to both action accessibility and the condition requiring the existence of all normalizers, weakly-action-representability is not necessarily inherited by Birkoff subcategories.
Keywords: weakly action representable, semi-abelian
2020 MSC: 18E13
Theory and Applications of Categories, Vol. 44, 2025, No. 8, pp 272-276.
Published 2025-02-13.
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