I have three questions.
Does the groupification of a semigroup always exist? I believe this should be yes because for every $x$ in the semigroup one could just define an element $x'$ that should work as its inverse. But what would then happen to the product $x'y$ for $x,y$ elements of the semigroup? It feels like we get choices (or maybe not) here that messes things up.
When defining the groupification, $G$, of a semigroup $S$ one require it to come with a morphism (of semigroups) $S \rightarrow G$ such that any other morphism (of semigroups) from $S$ to another group $G'$ factorizes through the previous map. Exactly which type of objects can be groupified? I guess one cannot groupify a topological space.
This is a broad question but is there some sense of -ification? In the example one could replace "group" by "topological space" and talk about topologyfication. Now, no such word seem to exist so I guess one could not "topologyfy".
We can (i think) consider the groupification functor from the category of semigroups to the category of groups and it should be adjoint to the forgetful functor from the category of groups to the category of semigroups. This would suggest that we need some sense of a forgetful functor in the first place to talk about a -ification.
Apologies for this bad question, sometimes asking the right question is just as hard as answering it.