The Donaldson-Thomas invariants count stable coherent sheaves on Calabi-Yau 3-folds which were introduced by Thomas around 1998. Later Joyce-Song, Kontsevich-Soibelman and Davison-Meinhardt introduced integer valued invariants, called BPS invariants, which also take account of strictly semistable sheaves. The BPS invariants play important roles in modern enumerative geometry. In this talk, I will introduce (quasi-)BPS categories for Higgs bundles. They are regarded as categorifications of BPS invariants of local curves (which are non-compact Calabi-Yau 3-folds), and are regarded as non-commutative analogue of Hitchin integrable systems. I will propose a conjectural symmetry of BPS categories which swaps Euler characteristic and weight, inspired by Dolbeaut Geometric Langlands equivalence of Donagi-Pantev, by the Hausel-Thaddeus mirror symmetry for Higgs bundles and χ-independence phenomena for BPS invariants of curves on Calabi-Yau 3-folds. I will give some evidence of the above conjecture for rank two cases and for topological K-theories. This is a joint work with Tudor Padurariu.