Image of a category under a functor need not be a category?
Can it happen that the image of a functor is not a category?
Big Endian vs. Little Endian in Qiskit I've noticed that Q# favors Little Endian. Meaning that most operations are designed for this type of encoding.  Is is it the same with Qiskit? Conjunction Puzzle: Is this clause dependent or independent? Third grade teacher here. I plan to teach students to distinguish between simple, compound and complex sentences — but only if I can demonstrate a clear and meaningful difference between the latter two!  Complex or Compound? Each sentence in the following pairs is similar to its partner.   All dogs are mammals, so huskies are mammals. All dogs are mammals, therefore huskies are mammals. I come bearing soup, for Kate is sick. I come bearing soup, because Kate is sick.   Are the sentences above complex or compound?   First, we need to decide whether each italicized clause is independent or dependent. To me, they all look dependent. If that is the case, there's not much need to teach about compound sentences. Is there a meaningful difference between the sentences in each pair that I am missing? (Are the FANBOYS as special as they'd like to think?) How do I change my username? Some time ago, when I installed Ubuntu, I chose a rather stupid username for my account that I do not want to use anymore. How do I change this (including the name of my home directory, and the name in the terminal) without losing settings for applications? How do I keep permissions and my keys for various authentification (e.g. email, SSH, GPG and more)? What settings could possibly get lost if I changed my username? Why was Count Dooku not given the title "Darth"? I don't know the exact significance of the word "Darth" in the Sith world, but I think it was a word of honor for powerful Sith. That's why Anakin was given this word in his new name.  All powerful Sith in canon had this word in their names: Darth Plagueis, Darth Bane, Darth Sidious, Darth Vader, Darth Maul, etc. As such name similarity can't be names given by their parents, I can assume they were given such words in names as a honor.   Now, look at Count Dooku... he was a powerful Sith too. So, why wasn't he given this title?    Darth word to address Dooku hasn't been used in the movies, as far as I know. If you are claiming that Darth and Lord words are same, give citations because my vocabulary rejects it. Indiscernible to create descending chain of elementary models Is it possible to disable CPU throttling on a MacBook Pro with a completely dead (not recognized) battery? I have a MBP late 2011 running El Capitan, recently my battery died (x over the icon and "no battery available" in the dropdown.) I've noticed since then that CPU intensive tasks are very slow, and I read that without a battery macs will throttle the CPU to half capacity.  So now I'm looking for one of two solutions:  1) Either somehow disable the throttling, or  2) Trick the computer into thinking it has a battery.  In regard to the first one I've tried a few things such as described , removing a plist file that supposedly controlled it, but that hasn't helped. Any help would be greatly appreciated, TIA.  Edit: I've looked over the question about a 2006 MacBook, it's similar but I've tried everything outlined there and nothing has worked. I'm curious if there are any new ideas. I think the difference may be El Capitan. I am trying to count the number of bit-strings of length 8 with 3 consecutive zeros or 4 consecutive ones. I was able to calculate it, but I am overcounting. The correct answer is $147$, I got $148$.  I calculated it as follows:  Number of strings with 3 consecutive zeros = $2^5+5\times2^4 = 112$, because the 3 zeros can start at bit number 1, 2, 3, .., 6  Number of strings with 4 consecutive ones = $2^4+4\times2^3 = 48$, I used the same reasoning.  Now I am trying to count the number of bit-strings that contain both 3 consecutive zeros and 4 consecutive 1s. I reasoned as follows:   the strings can be of the following forms: 0001111x, 000x1111, x0001111..thus there are $2+2+2 = 6$ possibilities for bit-strings where the 3 consecutive zeros come first. Symmetrically there are $6$ bit-strings where the 4 consecutive ones come first.  Thus the answer should be = $112+48-12 = 148$.  clearly there's something wrong with my reasoning, if someone could point it out, that would be awesome. Thanks Let $\{a_n\}$ be defined as follows: $$a_1 = 2, a_{n+1}=\dfrac{1}{3-a_n}$$ $n \geq 1$.   Does $\{a_n\}$  converge?    Using the monotone convergence thereom, if the sequence is both bounded below and decreasing, $\forall n\in\mathbb{N}, n\geq 1$, then we can say the sequence converges.  I'm having trouble proving that the sequence is bounded below by induction.    Claim: The sequence is bounded below by $0$.  Base Case:  $n=1$  $a_1 = 2 \geq 0$, so this holds.  Induction Step  Suppose that $a_k \geq 0$, for some $k \in\mathbb{N}$. (IH)  Prove $a_k \geq 0\to a_{k+1} \geq 0$  I have some difficulty here.  $a_{k}=\dfrac{1}{3-a_{k-1}} \geq 0$  $a_{k+1}=\dfrac{1}{3-a_{k}}$, but we know $a_k \geq 0$, but we don't know how much bigger. It could be that $a_k = 4$, and then I have $a_{k+1}=\dfrac{1}{3-4}$, which is negative, and does not confirm with my claim of being bounded below by $0$. Have I gone somewhere wrong in my induction? How to Screen Sharing / VNC to an iMac without waking the display? I have an iMac mid 2011 at home. When I was not home, I may need to access my mac with Screen Sharing. However the iMac display will turn itself on when I connect via Screen Sharing. The problem is I don't want to scare my family at home (with the elders and kids) as the iMac "turn itself on suddenly".   This is a problem specific for iMac. On MacBooks (Pro, Air, whatever) I can set the brightness to the lowest setting so the screen is black (i.e. the LED light is off). However on an iMac you cannot turn off the LED backlit by setting brightness. The display is still bright and everything is clearly visible even on lowest brightness setting.  Therefore these solution are not working as the display will turn on as soon as you move your mouse or hit any key on the keyboard via Screen Sharing.   Sleep Display (by Ctrl+Shift+Eject) Using the code listed on    Question: Is the a way to keep the iMac display off entirely while you accessing it with Screen Sharing? Block of equations with only some being subequations I'm trying to make a block of equations where the first two are standalone equations, and the second two are subequations, ie  X=XXXX (1)  X=XXXX (2)  X=XXXX (3a)  =XXXX (3b)  I'm using the amsmath package, with align and subequation, but I can't figure out how to do this without making a separate block for Eqs 1-2 and one for Eqs 3a-3b. That solution is unsatisfactory, because then there is a big vertical gap between the two blocks, and I want them to appear all as one.  Here's the code I have so far, in case it's unclear.  \begin{align} T(x) &amp;= \frac{m}{2{k_{B}}} \left\langle \mathbf{\tilde{v}}{(\mathbf{x}_{i},t)}^{2} \right\rangle\\  \mathbf{u}(x) &amp;= \left\langle \mathbf{v}_{i}(\mathbf{x}_{i},t) \right\rangle \end{align} \begin{subequations}  \begin{align} P_{xy}(x) &amp;= \frac{1}{A} \left\langle \sum\limits_{i} {m \tilde{v}_{i,x} \tilde{v}_{i,y}} + \frac{1}{2} \sum\limits_{i} {\sum\limits_{j\ne i} {r_{ij,y} F_{ij,x}}} \right\rangle \\ \begin{split}  &amp;=\frac{m}{A} \Bigg\langle \sum\limits_{i}{{{{\tilde{v}}}_{i,x}}{{{\tilde{v}}}_{i,y}}} + \frac{a^3\omega _{pd}^2}{4} \\  &amp;\quad \times \sum\limits_{i}{\sum\limits_{j\ne i}{r_{ij,y}{\left\{ \frac{e^{(-{{r}_{ij}}/\lambda )}}{{{r}_{ij}}}\left( \frac{1}{r_{ij}}+\frac{1}{\lambda} \right) \right\}_{x}}}} \Bigg\rangle \end{split} \end{align} \end{subequations}   Any suggestions would be greatly appreciated! What are the rules for China's visa-free transit programs? Why must local variables have initial values? I asked  that turned out to have multiple correct answers. How do I pick between them to determine which to accept?  All of the answers were different. They were not the same answer given multiple times. The the title is self explanatory, I guess.  Why can two (or more) electric  never cross? Adding shapefile or feature class as layer in ArcMap using ArcPy NOTE: I am not interested in calling /secur/logout.jsp since it ends all the active salesforce sessions.  I am developing a web application that is registered on salesforce as a connected app, so I am using salesforce credentials to authorize the user.  Application is developed in REST API and the communication with salesforce is happening in restful manner.   Auth url:   Authorization:  Method 1: If there is no salesforce session active, The user is taken to salesforce login page, where he enters his salesforce details to be authorized and after which he is taken to home page of my web application.  Method 2: If there is already a salesforce session active in another tab, the user is directly authorized and is taken to home page of my web application.  Now I am trying to implement logout button for my application, such that the following scenarios are covered,  Scene 1: The user is authorized using method1, and the user press the logout. Upon trying to logback the user is prompted for credentials.  Scene 2:  The user is authorized using method2, and the user should use logout to logout of the web application (not from active sessions). Upon login, the user should be again able to login using method2.  Can someone help me on how to implement the logout button such that it covers scenario 1 &amp; 2.  Thanks in advance. What "allocation unit size" should I use for a drive with a single NTFS partition? I'm formatting a 1TB external hard drive as a single NTFS partition.  This drive is mainly meant for storing media.  Should I choose something other than the default allocation unit size?  The options range from 512 bytes to 64K.  Are there any guidelines that I should use with partitions storing other data?  Should I stop poking around and just leave it at "default"? How do I center floated elements? Why would spacetime curvature cause gravity? Seeking alternatives to pgRouting for open source routing / network analysis?