Deformation theory tag info https://mathoverflow.net/tags/deformation-theory/info is very minimal and says almost nothing:

deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions $P_\epsilon$, where $\epsilon$ is a small number, or vector of small quantities.

Can some experienced user consider editing the tag info to make it better?

What I understood (from nlab) is the following.

A typical problem in deformation theory is the following :

Given a map $f:X\rightarrow Y$ (in a category), injective maps (monomorphisms) of special kind $i_X:X\rightarrow \tilde{X}$ and $i_Y:Y\rightarrow \tilde{Y}$ can we find a map $g:\tilde{X}\rightarrow \tilde{Y}$ such that $g\circ i_X=i_Y\circ f$. This map $g$ is called an infinitesimal deformation of $f$.

Does adding this content for tag info make it any better?