# Tag info for deformation theory tag

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?

• I will mention that this is one of the problematic tag-infos mentioned quite a long time ago in another meta posts (created by copying from another source without any attribution): Recent suggested tag wiki edits. (Also related to this problem: Should tag-wiki include a source where it is taken from?) It has been improved since then a bit - at least to include some links to the sources. – Martin Sleziak Dec 27 '18 at 10:46
• @MartinSleziak I do not know what to reply for you comment. I just wanted to say I read your comment :) Thanks. – Praphulla Koushik Dec 27 '18 at 12:53
• The nlab's definition is weird and idiosyncratic (like their definitions often are). Adding it to this tag would just make things confusing. – Andy Putman Dec 27 '18 at 19:20
• Also, the sentence in the tag info at present (I will edit it into the question above) is just bad writing. – David Roberts Dec 27 '18 at 20:04
• @DavidRoberts it is taken from Wikipedia article en.m.wikipedia.org/wiki/Deformation_theory – Praphulla Koushik Dec 28 '18 at 2:27
• @AndyPutman I am not experienced enough to comment about definitions given in nlab.. Can you take some time to write down tag wiki for this.. – Praphulla Koushik Dec 28 '18 at 6:00
• No, I don't have the time to edit tag info's -- what little time I have to spend here on MO I prefer to spend engaging in mathematics rather than moderation. – Andy Putman Dec 28 '18 at 17:39
• (I realize that participating in meta violates that policy somewhat; however, spending lots of time on minutia like tag info's would be far more of a time sink) – Andy Putman Dec 28 '18 at 17:41
• @AndyPutman Thanks for those wise words.. I have wasted so much time on this... I did not had any motivation/necessity to learn deformation theory nor any of the statements in wikipedia/n lab I understand.. I think it better to spend time on things that I find interesting (knowing what it is).. Thanks again.. :) – Praphulla Koushik Dec 29 '18 at 3:53

• So, what you are saying is.. we have a collection of objects $\{X(t)\}$ over some index set $\Lambda$ with $t\in \Lambda$.... There is also some compatibility depending on what $\Lambda$ is... if $\Lambda$ is a topological space then we want $X(t)$ to vary continuously and if $\Lambda$ is smooth we want $X(t)$ to vary smoothly and similarly in other cases.., now suppose $X(0)$ is a connected manifold we see if $X(\epsilon)$ is also connected manifold.. Is it something like that? If I don’t understand it is just that I did not understand, not that what you said is not reasonable... :) :) – Praphulla Koushik Dec 28 '18 at 11:22