My question refers to a statement in Laures' and Szymik's "Grundkurs Topologie" (page 233). Sorry, there exist only a German version. Here the relevant excerpt:    My question is why a category having a initial (or a final) object has a contractible classifying space?  Previously the author just shows that equivalent categories induce homotopy equivalent classifying spaces via   $$BC\times \Delta^1 \to BD$$.  Does this observation provide an answer of my question? Why?  Here the construction of classifying space with which the author works:, namely as a nerve of the functor $B:Cat \to \Delta^{op}-Sets, C \mapsto Mor(-,C)$:
Given a pointed category $X$, is $|N(X)|$ contractible ($N(X)$ is the nerve of $X$)? Or are there counter-examples?
Value of Vandermonde type determinant Let $x_1,...,x_n $ are distinct real numbers.  Is it a formula for the Vandermonde type determinant $V(x_1, \cdots,x_n)$  whose last column is $x_1^k,\ \cdots,\ x_n^k$, where $k \geq n$, instead of $x_1^{n-1},\ \cdots,\ x_n^{n-1}$?  Thanks Latexmk and the location of Asymptote's generated files I am trying out Asymptote with latexmk and I would like to automate the interaction.  Consider the following latex document test.tex:  \documentclass{minimal} \usepackage{asymptote} \def\asydir{asymptote}  \begin{document}  Testing Asymptote:  \begin{asy} settings.outformat = "pdf"; unitsize(2cm); draw((0,0) -- (1,0)); \end{asy}  \end{document}   In my latexmkrc I have the  for Asymptote integration:  sub asy {return system("asy -o asymptote/ \"$_[0]\"");} add_cus_dep("asy","eps",0,"asy"); add_cus_dep("asy","pdf",0,"asy"); add_cus_dep("asy","tex",0,"asy");   Running latexmk -pdf test.tex generates test.pdf in the current folder and test-1.asy and test-1.pdf in the asymptote folder -- but only if   I manually created the asymptote folder prior to running latexmk. The folder specification in the latex document (\def\asydir{asymptote}) and latexmkrc (-o asymptote/) are identical.   I would like latexmk to read asydir from the main tex file, create the directory if it does not exist and run asy with the read output folder.  Is this possible? For an odd prime $p$, prove that any primitive root $r$ of $p^n$ is also a primitive root of  $p$   So I have assumed $r$ have order $k$ modulo $p$ , So $k|p-1$.Then if I am able to show that $p-1|k$ then I am done .But I haven't been able to show that.Can anybody help me this method?Any other type of prove is also welcomed. Ownership of content in Community Wiki posts Make the chat link one click away in the new top bar What is the correct possessive for nouns ending in "‑s"? What do the nomodeset, quiet and splash kernel parameters mean? What do Kernel command line parameters (also also known as boot options) mean?  When you go to Ubuntu (or better, GRUB) options, you have things like nomodeset, quiet and splash. What do these options mean?  I am also interested in other parameters and would be interested to see descriptions of any kernel parameter (like acpi), but these are not essential. In Gmail, what is the safest way to download, save & print all emails with a given label? Attempting to securely download all the emails with a given label in Gmail, save them to a single file, and print that file. Dynamically fill an Enum with a list I'm writting an addon with an UI. In my draw function in my UI class I've this   layout.prop(bpy.context.scene, 'activebone', text='active bone')   Wich create an enum in the UI.    And in my register class I've this:  bpy.types.Scene.activebone = bpy.props.EnumProperty(items=active_bone)   In my draw fonction I fill the active_bone list with the some data and but the enum don't refresh himself. I know that i can retype  bpy.types.Scene.activebone = bpy.props.EnumProperty(items=active_bone)   But the draw function is Read only so I can't. Is it possible to refresh my Enum item in the draw function or am I obliged to do it in an other class like a button? Is there a way to draw a Voronoi diagram with pgfplots? I want to draw a voronoi diagram with pgfplots, but sadly I cannot get it the way it should look like. I used the Matlab command to get the x and y coordinates and saved them as a dat-file. In that file I stored the x coordinates in the first column and the y coordinates in the second column.      Does anyone have an idea, how it could work?  Minimal Example of the Code:  \documentclass{standalone}  \usepackage{amsmath,amsfonts,amssymb}  \usepackage{mathtools}  \usepackage[ngerman]{babel}  \usepackage[utf8]{inputenc}  \usepackage{graphicx}  \usepackage[svgnames]{xcolor}  \usepackage{pgfplots} \pgfplotsset{compat=newest}  \usepackage{tikz}  \usetikzlibrary{positioning,fit,calc,shapes,arrows,external,3d,patterns,spy}  \usepackage{filecontents}  \begin{document}  \begin{filecontents*}{data.dat}   -7.9265104e+00   3.6503989e-01    4.3133971e-01   9.4062409e-01   -7.9265104e+00   3.6503989e-01    6.3976919e-02   5.4947497e-01    6.3976919e-02   5.4947497e-01    3.0293735e-01   6.5037024e-01    3.6748619e-01   9.5786833e-02    6.3976919e-02   5.4947497e-01    3.0293735e-01   6.5037024e-01    4.0645496e-01   8.2958752e-01    4.9066479e-01   4.4410036e-01    3.0293735e-01   6.5037024e-01    3.6748619e-01   9.5786833e-02    4.9244296e-01   2.3488102e-01    4.9244296e-01   2.3488102e-01    4.9066479e-01   4.4410036e-01    4.9066479e-01   4.4410036e-01    7.3082954e-01   5.1825327e-01    1.8829507e+00   1.7053562e-01    4.9244296e-01   2.3488102e-01    4.3133971e-01   9.4062409e-01    8.7230061e-01   2.0371867e+00    4.0645496e-01   8.2958752e-01    4.3133971e-01   9.4062409e-01    6.6251849e-01   6.4842135e-01    4.0645496e-01   8.2958752e-01    6.9696115e-01   6.8938388e-01    8.7230061e-01   2.0371867e+00    7.3082954e-01   5.1825327e-01    6.6251849e-01   6.4842135e-01    1.8829507e+00   1.7053562e-01    7.3082954e-01   5.1825327e-01    6.6251849e-01   6.4842135e-01    6.9696115e-01   6.8938388e-01   -7.9265104e+00   3.6503989e-01   -1.7371176e+01   8.6111447e-02    3.6748619e-01   9.5786833e-02   -6.0998602e-02  -1.3709259e+00    1.8829507e+00   1.7053562e-01    4.4291165e+00  -2.9045575e-01    8.7230061e-01   2.0371867e+00    1.8287612e+00   4.5227847e+00    6.9696115e-01   6.8938388e-01    1.9370861e+00   1.3452721e+00 \end{filecontents*}  \begin{tikzpicture} \begin{axis}[x=3cm, y=3cm, z=0cm, view={0}{90}] \addplot3 [color=blue, samples y=0] file {voronoi.dat};  \end{axis} \end{tikzpicture}  \end{document}   Thanks for your help!! "Error: Invalid signature" when configuring dual boot Ubuntu 14.04 and Windows 10 How do the definitions of "irreducible" and "prime" elements differ? Install software from packages, or build it from source? Python, Unicode, and the Windows console When I try to print a Unicode string in a Windows console, I get an error . UnicodeEncodeError: 'charmap' codec can't encode character .... I assume this is because the Windows console does not accept Unicode-only characters. What's the best way around this? Is there any way I can make Python automatically print a ? instead of failing in this situation? Edit:  I'm using Python 2.5.  Note: @LasseV.Karlsen answer with the checkmark is sort of outdated (from 2008). Please use the solutions/answers/suggestions below with care!!  is more relevant as of today (6 Jan 2016). Does the std::stack in the C++ STL expose any iterators of the underlying container or should I use that container directly? I am wondering whether there is any difference between a gerund acting as subject and an infinitive acting as a subject. What exactly happens when you browse a website in your browser? What is the distance between the centers? Two unit circles overlap in such a way that exactly half the area of each circle is within the overlap. How far apart are the centers of the two circles? I know that nobody likes duplicate questions, but I haven't found my answer on any of the other questions with this topic.  I built a computer with a  (made by Gigabyte).  It supposedly has 512 CUDA cores.  I followed  tutorial, (which enabled the Nvidia proprietary drivers) and was able to enable dual monitors and all the desktop graphics that are needed.  Unfortunetly, the GPU processing option still doesn't show up in Blender.  I've tried installing nvidia-cuda-toolkit, and that didn't make a difference.  I also tried to update my drivers from nvidia-346 to nvidia-349, and this had no apparent effect either.  What can I do to enable GPU rendering?  (I've tried both blender installed and just downloaded from the site). Determining direction of longest segment of polygon using ArcGIS Desktop? I have a shapefile with 9000 agriculture fields and what I like to do is to determine for each field (=each polygon) the direction of the longest segment.  For instance, the selected polygon in the screenshot has its longest segment from west to east so I would like to mark give the polygon the attribute W (for west) or either E (for east).   Is there any solution to solve my problem in a fast but generalized way?   I do not need very detailed results. It's just for the interpretation of a question.   I'm seeking an answer using ArcGIS 10.2 for Desktop.  To be more precise on what I'm looking for I try to explain more practical: I'm doing winderosion analysis for a specific area with 9000 fields. As result I have a potential susceptibility for each field. I like to check, if the fields with high susceptibility are correlated to a certain orientation of the fields, e.g. check if most of the fields with high risk are oriented in the main winddirection or not.   The search for the longest segment is not really important for me. It was just an idea I had to determine the direction. So forget about the longest segment if there is a way to determine the direction with another method ;)