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A note on the relationship between action accessible and weakly action representable categories
Theory and applications of categories, Tome 44 (2025), pp. 272-276 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.
Publié le :
Classification : 18E13
Keywords: weakly action representable, semi-abelian 
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     author = {James Richard Andrew Gray},
     title = {A note on the relationship between action accessible and weakly action representable categories},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2025_44_a7/}
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James Richard Andrew Gray. A note on the relationship between action accessible and weakly action representable categories. Theory and applications of categories, Tome 44 (2025), pp. 272-276. http://geodesic.mathdoc.fr/item/TAC_2025_44_a7/