Injectivity and modelling in the Blass topos (Q1103043)

\textit{A. Blass} [Trans. Am. Math. Soc. 255, 31--59 (1979; Zbl 0426.03053)] invented an elementary topos \(B\) in which there are no non-zero injective abelian groups, contrary to our usual experience in the topos of (say) Gödel-Bernays with \(AC\) sets. This paper shows that for the interpretations in \(B\) of modules over any ring, Boolean algebras, and distributive lattices there are likewise no non-trivial injectives. On the other hand, the category of semilattices in \(B\) does have enough injectives, as do partially ordered sets and normed linear spaces (if injectivity is defined via embeddings rather than general monomorphisms).