What concept does a natural transformation between two functors between two monoids viewed as categories correspond to?
Group theoretic meaning of natural isomorphisms between certain functors
I have an internal microphone in my laptop. I think it uses Intel High Definition Audio. But I can't get it to work with Ubuntu. It doesn't work with either the Sound Recorder or Skype.  On the Input tab in 'Sound Preferences', I just see Internal Analog Input Device... How to evaluate this trigonometric limit? I have been struggling to solve this limit.  What is the limit as $x$ approaches $45^0$ of $$\frac{\sqrt{2}\cos x-1}{\cot x-1}?$$   I know how to use L'Hospital's rule to calculate this limit and got the answer as $0.5$. But, how do I calculate the limit by manipulating the function? Please provide only some hints to proceed. How to open a serial port by friendly name? When do we not put a comma before "because"? In what situation do you put a comma before "because"?   And, when do you not put a comma before "because"?   I've always assumed that you put a comma, because the clause introduced by "because" will always be independent, because it cannot stand on its own, because it wouldn't make sense on its own.   Is this the case? Could you think of an example where it doesn't take a comma? I have a MacBook Pro 2009 running MacOS El Capitan. Recently the Wi-Fi has stopped working.   When I click on the Wi-Fi icon it displays the message "No hardware installed", but Ethernet still works.   Is there any way of fixing this by using a Wi-Fi dongle or something of the sort, if so do I need a specific dongle and how do I install it? Getting an error while trying to script it, specifically "Cannot use VB for services."  Snippet and VB code block as follows:  Raw block (works within ArcMap): "\ftp\raw\YYYYMMDD\Files\Charles" +[NAME]+".ntf"  Snippet:      date = '"20160207"'      arcpy.CalculateField_management(outShp, "Link", '"\\\\ftp\\raw\\"' + date + '"files"' + "[NAME]"+ '".shp"', "VB", "")   Not sure what the issue is, somehow need to be able to insert the date and have it syntactically be correct (in either VB or python).  I didn't explain very well I have a column that contains a portion that is part of the hyperlink, so need to concatenate A column to the end of B column (with the partial path) to complete the link Currently using ubuntu 15.10 on azure and installed the gnome and vnc4server latest version on ubuntu. Please find log file below:  Current VNC client screen:    $ cat .vnc/myhost1\:1.log    --cut-- VNCSConnST:  Server default pixel format depth 16 (16bpp) little-endian rgb565 VNCSConnST:  Client pixel format depth 8 (8bpp) colour-map Window manager warning: Invalid WM_TRANSIENT_FOR window 0x20000c specified for    0x20000b (I        nitialization error). Error org.freedesktop.DBus.Error.NameHasNoOwner: Could not get owner of name    'org.gnome.ze        itgeist.Engine': no such name amdxdg-su: no graphical method available for invoking '/usr/bin/amdcccle' as 'root'  $ cat .vnc/xstartup unset SESSION_MANAGER  [ -x /etc/vnc/xstartup ] &amp;&amp; exec /etc/vnc/xstartup [ -r $HOME/.Xresources ] &amp;&amp; xrdb $HOME/.Xresources  vncconfig -iconic &amp;  gnome-panel &amp; gnome-settings-daemon &amp; metacity &amp; nautilus -n &amp; gnome-terminal &amp;   How to get 24bit color with wide screen (Now I getting square screen in vnc client) Change all file type associations from one program to another Is it possible to easily change all file type associations that are currently associated with one program to another program in one batch?  In my case, I am trying to change all files types currently associated with Notepad to instead use Notepad++ in Windows 7.  It's a pain to go through Default Programs &gt; Set Associations because after each type the entire list re-populates, taking several seconds.  Is there a way I can do a search and replace in the registry, or something even easier? What is the most efficient way to deep clone an object in JavaScript? What is the most efficient way to clone a JavaScript object? I've seen obj = eval(uneval(o)); being used, but . I've done things like obj = JSON.parse(JSON.stringify(o)); but question the efficiency.  I've also seen recursive copying functions with various flaws.  I'm surprised no canonical solution exists. $c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property] If $c$ is a common divisor of $a$ and $b$ then $c$ divides the greatest common divisor of $a$ and $b$.  What can we use to prove this? Does infinity exist in physical systems? How can I make it so that each space has its own isolated dock?  Basically what I'm looking for is:   The dock in one space should not show the icon of an app that was open in another space. If I have the same program open in two different spaces, clicking on the icon in one space should not go to the app in the other space.   Is this possible natively, or with a third party program? Where to get 2010 Census Block data? I would like to download 2010 Census Block Data for several towns and I can't seem to find it on American Factfinder.   Is it there? And if not, does anyone know where I could find it? "Coming soon" pages & SEO Given an array of n Objects, let's say it is an array of strings, and it has the following values:  foo[0] = "a"; foo[1] = "cc"; foo[2] = "a"; foo[3] = "dd";   What do I have to do to delete/remove all the strings/objects equal to "a" in the array? How do I deal with a compromised server? This is a  about Server Security - Responding to Breach Events (Hacking)   See Also:                  Canonical Version I suspect that one or more of my servers is compromised by a hacker, virus, or other mechanism:   What are my first steps? When I arrive on site should I disconnect the server, preserve "evidence", are there other initial considerations? How do I go about getting services back online? How do I prevent the same thing from happening immediately again? Are there best practices or methodologies for learning from this incident? If I wanted to put a Incident Response Plan together, where would I start? Should this be part of my Disaster Recovery or Business Continuity Planning?   Original Version       2011.01.02 - I'm on my way into work at 9.30 p.m. on a Sunday because our server has been compromised somehow and was resulting in a    attack on our provider. The servers access to the Internet   has been shut down which means over 5-600 of our clients sites are now   down. Now this could be an FTP hack, or some weakness in code   somewhere. I'm not sure till I get there.      How can I track this down quickly? We're in for a whole lot of   litigation if I don't get the server back up ASAP. Any help is   appreciated. We are running Open SUSE 11.0.            2011.01.03 - Thanks to everyone for your help. Luckily I WASN'T the only person responsible for this server, just the nearest. We managed   to resolve this problem, although it may not apply to many others in a   different situation. I'll detail what we did.      We unplugged the server from the net. It was performing (attempting to   perform) a Denial Of Service attack on another server in Indonesia,   and the guilty party was also based there.      We firstly tried to identify where on the server this was coming from,   considering we have over 500 sites on the server, we expected to be   moonlighting for some time. However, with SSH access still, we ran a   command to find all files edited or created in the time the attacks   started. Luckily, the offending file was created over the winter   holidays which meant that not many other files were created on the   server at that time.      We were then able to identify the offending file which was inside the   uploaded images folder within a  website.      After a short cigarette break we concluded that, due to the files   location, it must have been uploaded via a file upload facility that   was inadequetly secured. After some googling, we found that there was   a security vulnerability that allowed files to be uploaded, within the   ZenCart admin panel, for a picture for a record company. (The section   that it never really even used), posting this form just uploaded any   file, it did not check the extension of the file, and didn't even   check to see if the user was logged in.      This meant that any files could be uploaded, including a PHP file for   the attack. We secured the vulnerability with ZenCart on the infected   site, and removed the offending files.      The job was done, and I was home for 2 a.m.            The Moral   - Always apply security patches for ZenCart, or any other CMS system for that matter. As when security updates are released, the whole   world is made aware of the vulnerability.   - Always do backups, and backup your backups.   - Employ or arrange for someone that will be there in times like these. To prevent anyone from relying on a panicy post on Server   Fault. what is the area of the region [ (x,y):0<x , y<1 , 3/4<x+y<3/2 ]? This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, navigate to the  tag. This question and answer is owned by the community! If you can improve it and make it more useful, you're welcome to edit it. I am building a trigger, a unit test, or other Apex code. I'm working with sObject records, and trying to access related record information. For example, I might have a structure like this: Account a = new Account(Name = 'Test'); insert a;  Opportunity o = new Opportunity(Name = 'Donation', AccountId = a.Id); insert o;  System.assertEquals(o.Account.Name, 'Test', 'Correct Account associated'); // Assertion fails!  Or, in a trigger, I might be aiming for something like this: trigger ContactTrigger on Contact (after insert) {     for (Contact c : Trigger.new) {         if (c.Account.Name == 'Test') {             // Take some action here         }      } }  Why doesn't this work? Why am I getting null values, or NullPointerExceptions? Catalina not allowing to change read/write permissions despite having SIP disabled Currently Running: macOS Catalina 10.15.1 Issue: Ever since I upgraded to Catalina, macOS is not allowing me to change read and write permissions on system protected files, hence, I am not able to tweak the system as per my likes and dislikes. Steps Tried To Solve The Issue: SIP, always remains . So, no question arises regarding any conflict with system integrity protection. I have also tried to force change the permissions on the system files I want to edit using certain brute force commands, which I can't recall the name of, right now. But, I have tried. As of now, I am still unable to change read and write permissions on system protected files and resources. Axis with trigonometric labels in PGFPlots How do I make the axis labels use multiples of \pi in PGFPlots?