In this work, we provide a simple way to construct d-abelian categories via bounded derived categories for certain values of d. Namely, let C be an abelian category, and let C0, m denote the full subcategory of the bounded derived category of C whose objects X satisfy that H_* (X) is concentrated in degrees j where 0 j m. We prove that if C is hereditary, then C0, m is a d-abelian category where d = 3m + 1. Beyond offering a uniform method for constructing d-abelian categories, this construction allows us to create d-abelian categories that exhibit some unexpected properties depending on the choice of the category C. For instance, if C is the category of abelian groups, then C0, m is a d-abelian category which is not K-linear over a field K but has set indexed products and coproducts. Similarly, if C is the category of coherent sheaves over certain algebraic curves, then C0, m is a d-abelian category without enough injectives. We extend our results to (n+2) -angulated categories. Namely, let M be an n-cluster tilting object over an n-representation finite algebra and let T be the corresponding (n+2) -angulated category with n-suspension functor Σₙ. We prove that the full subcategory T0, m = add ^m₉=₀Σʲₙ M is a d-abelian category where d = (n+2) (m+1) -2. Furthermore, we show that there is a bijection between the functorially finite wide subcategories of add\, M and the functorially finite repetitive wide subcategories of T0, m.
Jørgensen et al. (Mon,) studied this question.