Several additive categories arising in applications fail to be abelian but are only semi-abelian, that is, the morphism \(\bar{f}: \mathrm{coim} f \to \mathrm{im} f \) in the canonical decomposition \(f: A\to \mathrm{coim} f \to \mathrm{im} f \to B\) is as well a mono- as an epimorphism but in general not invertible. A typical example is the category of \textit{topological} abelian groups where \(\bar{f}\) is always a bijection but its inverse need not be continuous. Although many homological constructions go through in semi-abelian categories there are arguments using pullbacks and pushouts which do not only rely on the corresponding universal properties. One is then led to \textit{quasi-abelian} categories where, by definition, cokernels are stable under pullbacks and kernels are stable under pushouts. Fortunately, in many concrete categories these additional stability conditions hold automatically, and the Raikov-conjecture had been that this is always so. This conjecture was disproved in the category of bornological locally convex spaces (that is, inductive limits of normed spaces) by \textit{S. Dierolf} and \textit{J. Bonet} in 2005 [``The pullback for bornological and ultrabornological spaces'', Note Mat. 25(2005/2006), No.~1, 63--67 (2006; Zbl 1223.46003)]. In 2008, \textit{W. Rump} published a different counterexample [``A counterexample to Raikov's conjecture'', Bull. Lond. Math. Soc. 40, No. 6, 985--994 (2008; Zbl 1210.18010)]. The present article contains a very thorough comparison of semi- and quasi-abelian categories. In particular, it is shown that every semi-abelian category has as a left (or right) essential embedding into a quasi-abelian category such that it can be recovered by localization. Moreover, it is characterized when a left- or right-essential semi-abelian subcategory of a quasi-abelian category is again quasi-abelian. This criterion is then applied to the categories \({\mathcal B}or\) and \({\mathcal B}ar\) of bornological and, respectively, barelled locally convex spaces which are right-essential subcategories of all locally convex spaces. Whereas Bonet and Dierolf's example disproving Raikov's conjecture was a countable inductive limit of Banach-spaces, the author obtains now different examples in the realm of spaces of continuous functions on ``strange'' topological spaces.