Mutación de complejos cosilting de dos términos usando categorías extrianguladas
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English translation of the abstract: A torsion pair is a way of “twisting” a category into two “orthogonal” subcategories which we can further “untwist” in order to recover the whole category, allowing us to study it in its entirety via simpler portions of it. Each torsion pair provides a unique way of decomposing the category, by which the ability to change or “mutate” from one to another can be of great use. For an associative unital ring $R$, torsion pairs in $\text{mod}(R)$ are in bijection with two-term cosilting complexes, a special class of complexes of injective $R$-modules. Recently, a general theory of mutation of cosilting objects in triangulated categories with products was introduced in [ALSV25]; however, when applying it to the bounded homotopy category of injective $R$-modules in order to mutate a two-term cosilting complex, there are no guarantees that the resulting cosilting object is of the same type. In this talk, we present recent work in which we show how, by changing our focus to the extriangulated category of large injective copresentations $\mathcal{K}^{[0,1]}(\text{Inj}R)$, we can restrict the previous operation to one of mutation between two-term cosilting complexes. Links: slides.