  For a fixed finite dimensional algebra $A$, we study representation
embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called
homological, if it induces an isomorphism on all Ext-groups and weakly
homological, if only Ext$^1$ is preserved. In case $A$ is a preprojective
algebra of Dynkin type, we give an explicit classification of all weakly
homological and homological embeddings. Furthermore, we show that for
self-injective algebras a classification of homological embeddings becomes
accessible once these algebras fulfil the Tachikawa conjecture.
