44 citations · 110 across the 20 of their papers we have counts for
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A Grothendieck category with a noetherian generator and exact products that is not a module category
Ryo Kanda
We construct a Grothendieck category that has a noetherian generator, satisfies AB4*, and is not equivalent to a module category. This gives a negative answer to Djament's problem.…
Module-theoretic approach to dualizable Grothendieck categories
Ryo Kanda
We prove that every dualizable Grothendieck category whose dual is again a Grothendieck category satisfies Grothendieck's conditions Ab6 and Ab4*, by taking a module-theoretic appr…
Non-exactness of direct products of quasi-coherent sheaves
Ryo Kanda
For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct products in the category of quasi-coherent sheaves are not exact unless the scheme is a…
Extension groups between atoms in abelian categories
Ryo Kanda
We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelope…