Geodesic
Distributive categories of coalgebras
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 363-373

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We prove that the category of coalgebras for an endo-functor F is distributive or extensive, provided that F preserves pullbacks along monomorphisms and the underlying category is distributive or extensive.
Keywords: coalgebra, coproduct, distributive category, pullback 
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Mavoungou, Jean-Paul. Distributive categories of coalgebras. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 363-373. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a12/