Properties of the categories $\textup{\textsf{cat}}$ of abelian groups, or $\textup{\textsf{cat}}_R$ of modules over a unital ring, or $\textup{\textsf{cat}}_R$ of chain complexes of $R$-modules are abstracted in the notion of an abelian category. Abelian categories were introduced by Buchsbaum \cite{buchsbaum-exact} and developed by Grothendieck \cite{tohoku} with the aim of unifying the ``coefficients’’ of the various cohomology theories then under development.