# Thick subcategories and semistability for projective presentations

For every finite dimensional algebra, there are correspondences between support \tau-tilting modules, functorially finite torsion pairs, and left finite wide subcategories of the module category. The first two classes of objects have “mirror” versions in the category of projective presentations, namely, 2-term silting complexes and cotorsion pairs. In this talk, we propose that the analog of the third class of objects is that of thick subcategories. We will recall the notion of a thick subcategory of the category of projective presentations and show that those with enough injectives are in bijection with left finite wide subcategories. We will explain how thick subcategories arise from an attempt to define semistability for projective presentations.