Add to ORKGFor a certain class of abelian categories, we show how to make sense of the \u27Euler characteristic\u27 of an infinite projective resolution (or, more generally, certain chain complexes that are bounded only above), by passing to a suitable completion of the Grothendieck group. We also show that right-exact functors (or their left-derived functors) induce continuous homomorphisms of these completed Grothendieck groups, and we discuss examples and applications coming from categorification. © 2012 London Mathematical Society
AbstractWe give a unified approach to various forms of completion of abelian groups. The relationshi...
When the exact completion of a category with weak finite limits is a Mal’cev category, it is possibl...
Let A be a finite-demensional k-algebra over an algebraically closed field k. We denote by mod A the...
In this paper, we first introduce stable functors with respect to a complete cotorsion pair and inve...
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Let $G$ be a $p$-adic Lie group with reductive Lie algebra $\mathfrak{g}$. Denote by $D(G)$ the loca...
We study elementary Tate objects in an exact category. We characterize the category of elementary Ta...
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We develop the theory of exact completions of regular $\infty$-categories, and show that the $\infty...
The Grothendieck group is an interesting invariant of an exact category. It induces a decategoricati...
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The Godement cosimplicial resolution is available for a wide range of categories of sheaves. In this...
AbstractWe give a unified approach to various forms of completion of abelian groups. The relationshi...
When the exact completion of a category with weak finite limits is a Mal’cev category, it is possibl...
Let A be a finite-demensional k-algebra over an algebraically closed field k. We denote by mod A the...
In this paper, we first introduce stable functors with respect to a complete cotorsion pair and inve...
AbstractWe demonstrate an equivalence between general types of Grothendieck categories and specific ...
Let $G$ be a $p$-adic Lie group with reductive Lie algebra $\mathfrak{g}$. Denote by $D(G)$ the loca...
We study elementary Tate objects in an exact category. We characterize the category of elementary Ta...
Let k be an algebraically closed field of characteristic 0. We denote by C the abelian k-category wh...
AbstractA generalization of the definition of the pro-category Pro-C for a category C is introduced,...
We develop the theory of exact completions of regular $\infty$-categories, and show that the $\infty...
The Grothendieck group is an interesting invariant of an exact category. It induces a decategoricati...
AbstractA generalization of the definition of the pro-category Pro-C for a category C is introduced,...
AbstractUsing the exact completion of a weakly left exact category, we specialize previous results o...
AbstractAs Spaltenstein showed, the category of unbounded complexes of sheaves on a topological spac...
The Godement cosimplicial resolution is available for a wide range of categories of sheaves. In this...
AbstractWe give a unified approach to various forms of completion of abelian groups. The relationshi...
When the exact completion of a category with weak finite limits is a Mal’cev category, it is possibl...
Let A be a finite-demensional k-algebra over an algebraically closed field k. We denote by mod A the...