How can I delete the word `Category:` from page titles?
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What good are free groups? In , one learns two definitions of free groups associating with sets.        Let $A$ be a set, the free group of $A$, $F(A)$ is the initial object in the category $\mathcal{C}$, where \begin{equation} \operatorname{Obj}(\mathcal{C})=\{A\xrightarrow{g}G\}, \end{equation}where the codomain $G$ are groups, and \begin{equation} \operatorname{Hom}(\mathcal{C})=\{\text{Commutative Diagrams } A\xrightarrow{g_1}G_1\xrightarrow{\phi}G_2\xleftarrow{g_2}A\}  \end{equation} where $\phi$ are group homomorphisms.   Also $F(A)$ has the concrete construction with elements being non-redundant words with alphabet $A$, and the group multiplication being juxtaposition and reduction.      But what good are free groups? Why are they useful?  says they are useful in topology, but does not explain why explicity.   Can someone give some examples that an undergraduate can understand? I am asking about examples that can show the usefulness of this abstract construction. So I guess the identification of $\mathbb{Z}=F({a})$ does not really count. Is there a name for this type of sentence structure: "She looks as though she's been poured into her clothes, and forgot to say 'when'"? Comedians seem to use phrases that employ this type of sentence structure - is there a name for it?  Examples of Groucho Marx's one liners seem to fit this pattern — and if memory serves, Emo Philips.       One morning I shot an elephant in my pajamas, how he got in my pajamas, I don't know.     I've had a perfectly wonderful evening, but this wasn't it. Why is file transfer speed decreased when copying multiple smaller files? Let's say I'm copying a portable apps directory from PC to an external HDD. An application.exe file is around 4 megabytes in size, but most other files are only tens of kilobytes in size, and most of those files take longer to copy/move than that bigger file having 4 megabytes.  Why is this? How can I make my IP address appear to be from another country? How do I make it appear that my IP address is coming from one country while I'm located in another? I live in Germany and some websites (like Hulu or Youtube) don't work because my IP isn't in the US. How do I get around this? Do I have to use a proxy or something?  Moderator note Super User does not endorse nor defend any activity which may be used to circumvent local/state/national laws. On Linux can I keep a program running in background even after I disconnect? If I'm logged into a remote Linux machine, I know I can suspend a process (cntr-z) and move it to the background (bg 1) but if I disconnect from the machine, the process stops.  Is there a way I can leave it in the background and have it there when I log back in? This is a very long running process.  On Ubuntu, logged in via SSH. What is the difference between Parse() and TryParse()?  int number = int.Parse(textBoxNumber.Text);  // The Try-Parse Method int.TryParse(textBoxNumber.Text, out number);   Is there some form of error-checking like a Try-Catch Block? What makes a bread either close or open crumbed/textured? What causes the texture of bread to be open, ie with lots of large holes, or close, ie a regular, uniform tender crumb with no large holes? How can I achieve either? I have several covariates in my calculation for a model, and not all of them are statistically significant.  Should I remove those that are not?  This question discusses the phenomenon, but does not answer my question:   There is nothing in the answer to that question that suggests that non-significant covariates be taken out, though, so right now I am inclined to believe that they should stay in.  Before even reading that answer, I was thinking the same since a covariate can still explain some of the variance (and thus help the model) without necessarily explaining an amount beyond some threshold (the significance threshold, which I see as not applicable to covariates).  There is another question somewhere on CV for which the answer seems to imply that covariates should be kept in regardless of significance, but it is not clear on that.  (I want to link to that question, but I was not able to track it down again just now.)  So...   Should covariates that do not show as statistically significant be kept in the calculation for the model?  (I have edited this question to clarify that covariates are never in the model output by the calculation anyway.)  To add complication, what if the covariates are statistically significant for some subsets of the data (subsets which have to be processed separately).  I would default to keeping such a covariate, otherwise either different models would have to be used or you would have a statistically significant covariate missing in one of the cases.  If you also have an answer for this split case, though, please mention it. Is it possible to redirect connections to a specific IP/port to an external IP/port?  Example:   Server A has the external IP xxx.xxx.xxx.xxx Server B has the external IP yyy.yyy.yyy.yyy User sends a request to server A on port 2106, I want to redirect it to server B at port 2106. How do I disable a bottom panel with the list of open windows on GNOME 3? How do I disable "Workspace dock" (a bottom panel with the list of open windows and a workspace indicator-cum-switcher), the one that is over "Plank" in the screenshot below?    I'm using Ubuntu 17.10. What is the difference between linear regression on y with x and x with y? The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the same, but I don't think that's the case.   Can someone shed light on when the relationship is not symmetric, and how that relates to the Pearson correlation coefficient (which I always think of as summarizing the best fit line)? Preventing brute force attacks against ssh? What tool or technique do you use to prevent brute force attacks against your ssh port. I noticed in my Security logs, that I have millions of attempts to login as various users through ssh.  This is on a FreeBSD box, but I imagine it would be applicable anywhere. Horizontal line inside a matrix I tried to make a horizontal line inside a matrix by the attached code. However, it didnot work the compiling process gives a time out message. It work normally without the \hline command. Any help!  \documentclass[journal,draftcls,onecolumn,12pt,twoside]{IEEEtran} \usepackage{array} \usepackage{blkarray} \begin{document} \begin{equation}  \centering W_b(1)=\begin{blockarray}{cccccc} \begin{block}{(ccccc)c}  a      &amp; b     &amp;     &amp;  &amp;  &amp; \matindex{\leftarrow d=0} \\ \ddots &amp; \ddots&amp;     &amp;  &amp;  &amp; \matindex{\vdots} \\    &amp;     a &amp; b   &amp;  &amp;  &amp; \matindex{\ \ \ \   \leftarrow d=d_b-1} \\   %\hline  c      &amp; d     &amp;     &amp;  &amp;  &amp; \matindex{\leftarrow d=d_b} \\   \ddots &amp;\ddots &amp;     &amp;  &amp;  &amp; \matindex{\vdots} \\    &amp;   c   &amp;  d  &amp;  &amp;  &amp; \matindex{\leftarrow d=D}  \end{block} \end{blockarray}, \label{eq:eq4}  \end{equation}  \end{document} Seeking options for Spatial ETL (Extract, Transform, Load)? I am interested in the pros and cons of various spatial ETL (extract, transform, load) tools.  If you have used the items listed here (or add your own), I seek your opinions and experiences.  In particular I would like to see usability comparisons of:    (proprietary)  (proprietary, subset of FME features)  (open source)  (open source)  (I don't know that it is truly ETL, but more of a file translation toolset) Any additional lot listed   There is no need to give a review of ALL software mentioned.  If you are experienced with even one then that will be very beneficial in making a decision about which direction to go.  Example: I am looking to create a schema conversion function that will allow me to select the input layer, create a translation, and output to a new, pre-defined schema.  Optimally, after creating the translation script, I would like to have an interactive form where I can "map" fields in my input layer to the output layer (ie- The output layer will have a field called "Address", what is it called in the input layer?)  Some were mentioned in the Q&amp;A at   And here are a couple of related articles that I found. The Android OS monitors the power consumption of running apps and hardware (display). As you may guess, this is a useful feature as it allows to track down energy greedy apps.  Is there an application that would do such monitoring on Mac OS?  It should calculate the percentages of the charge that an application/process/hardware has used.  I use plenty of little software that runs in the background permanently. It would be nice to know if such little helpers drain the battery significantly. What happens to Bucky's arm at the end of Infinity War? Bucky (Winter Soldier) has a metal arm (possibly made from vibranium?) but it's an attachment to his body as far as I understand. Why, when Thanos destroys half of the universe at the end of Infinity War, does his metallic arm also disappear with him? Shouldn't it be left behind as his gun did? Anyone on the Android Jelly Bean OS and not able to buy Apps/Books through wallet? I have just bought the Samsung GalaxyNote 800 and am facing this issue.   The error is (RPC:S-7:AEC-0).   What is the solution? Grub does not show a Windows 8 option after dual boot Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective Let $f: A \rightarrow B$ be a function. How can we show that for all subsets $S$ of $A$, $S \subseteq f^{-1}(f(S))$? I think this is a pretty simple problem but I'm new to this so I'm confused.  Also, how can we show that $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective? How do I make ditto marks? In France, students are taught not to repeat the same text twice when there is little difference between a line and the one below. It's a quick way to take notes.  I reproduced this effect by tinkering:    The code is as follows:  \documentclass[aspectratio=1610]{beamer}  \usepackage[T1]{fontenc} \usepackage[french]{babel}  \usepackage{amsmath, amsfonts, amssymb} \usefonttheme[onlymath]{serif}  \begin{document} \begin{frame} Lorsque le \og \textit{carreau carré} \fg{}   mesure: \begin{itemize} \item $\rm 1\,cm$ de côté, l'unité d'aire est appelée le \og \textrm{centimètre carré} \fg{} et est noté $\rm cm^2$; \item $\rm 1\,dm$ \hspace{1mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}''\hspace{8mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{décimètre carré} \fg{} \hspace{2mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1.5mm} $\rm dm^2$; \item $\rm 1\,m$ \hspace{3mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}'' \hspace{7mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{mètre carré} \fg{}  \hspace{9mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1mm} $\rm m^2$; \item etc. \end{itemize} \end{frame} \end{document}   How can I get the same effect more simply than by tinkering like I just did?