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For function germs $g:(\mathbb C^n,0)\to (\mathbb C,0)$ it is well known that$1\leq\frac{\mu(g)}{\tau(g)}$ and it has recently been proved by Liu that$\frac{\mu(g)}{\tau(g)}\leq n$. We give an upper bound for the codimension ofmap-germs $f:(\mathbb C^n,0)\to (\mathbb C^p,0)$ given as augmentations ofother map-germs with which we prove the analog to the first inequality (knownas Mond's conjecture) for augmentations $h:(\mathbb C^n,0)\to (\mathbbC^{n+1},0)$. Furthermore, we show that the quotient given by the image Milnornumber and the codimension of any augmentation in the pair of dimensions$(n,n+1)$ is less than $\frac{1}{4}(n+1)^2$ and prove the analog to the secondinequality for map-germs with $n=1$ and augmentations with $n=2,3$. We thenprove a characterization of when a map-germ is an augmentation, finding acounterexample for the characterization given by Houston. Next, we givesufficient conditions for when the augmentation is independent of the choice ofstable unfolding by studying different notions of equivalence of unfoldings.Moreover, these results allow us to give sufficient conditions for thesimplicity of an augmentation, providing context to locate the moduli fornon-simple augmentations.

Augmentation of singularities: $\mu/\tau$-type conjectures and simplicity