From MacLane's Category Theory:  A group is a category with one object in which every arrow has a two-sided inverse under composition.  So the analogies I see between a category group $CG$ and a group $G$ is as follows:  Arrows : Elements of the group Identity arrow : identity element composition of arrows : group operation Associativity function : associative group operation Unit law : identity properties All composable arrows exist : closure of the group  But the one I can't seem to understand is: What is analog for the single object in $CG$?  Single object in category : (Something for a group)?
A groupoid is defined to be a category where every morphism is an isomorphism. So sometimes a group is said to just be a groupoid with one object.   When I try to make sense of this, I denote the single object as $G$. I view the morphisms as the analogue of "elements." The identity $1_G$ is the analogue of the usual identity $e$, we can compose any two morphisms since they are all arrows on $G$, and for any arrow $f$, we have some $f^{-1}$ such that $f\circ f^{-1}=f^{-1}\circ f=1_G$, so the idea of inverses is still there.  So I informally associate the elements of the group in the usual definition to be the arrows in the groupoid. But what does the sole object $G$ in the groupoid "correspond to" if I were to try to informally make sense of a group in the usual sense? Does it even correspond to anything?
Grepping logs for IP addresses Proper use of the IDisposable interface I know from reading  that the "primary" use of the IDisposable interface is to clean up unmanaged resources.  To me, "unmanaged" means things like database connections, sockets, window handles, etc.  But, I've seen code where the Dispose() method is implemented to free managed resources, which seems redundant to me, since the garbage collector should take care of that for you.  For example:  public class MyCollection : IDisposable {     private List&lt;String&gt; _theList = new List&lt;String&gt;();     private Dictionary&lt;String, Point&gt; _theDict = new Dictionary&lt;String, Point&gt;();      // Die, clear it up! (free unmanaged resources)     public void Dispose()     {         _theList.clear();         _theDict.clear();         _theList = null;         _theDict = null;     }   My question is, does this make the garbage collector free memory used by MyCollection any faster than it normally would?  edit:  So far people have posted some good examples of using IDisposable to clean up unmanaged resources such as database connections and bitmaps.  But suppose that _theList in the above code contained a million strings, and you wanted to free that memory now, rather than waiting for the garbage collector.  Would the above code accomplish that? We learned in Thor: Ragnarok that Mjolnir is only a focus for Thor's power, not the source. If so, when a worthy​ being lifts Mjolnir and gains "the power of Thor", where are they getting the power from? What is the difference between <%# and <%= in ASP.NET MVC? How did Rita know she lost the power? Are files created in "/storage/emulated/0" supposed to appear in "/storage/sdcard0"? From what I guess, internal storage is available by every user. If emulated storage is a storage location, made for a specific user, are files created in /storage/emulated/0 supposed to appear in /storage/sdcard0? I assume no, because files that are user created should show up in emulated only, otherwise files created by the user would be available for all other users to see. What is the best term to describe the fact that most users have an initial dislike of any change to a UI even though it may really be net better over time?  Note: Question originally appeared Can't log in using Firefox in Stack Overflow Here's what is happening; everytime I go to Stack Overflow (stackoverflow.com, NOT meta) with Firefox, it gives me the "Welcome back" tab that pops up from the top. Whenever I click in the "click here to refresh the page" link, all it does is refresh the page without logging me back in.  Even if I try to log in using the "log in" button at the top, all it does is pop up the tab that says "Welcome name here, you're being redirected." The problem is I'm not being logged in, not to mention that it keeps refreshing the page over and over again without giving me a choice to log in with Facebook.  For some reason, I was capable of logging in to Meta Stack Overflow using Firefox. I am still unable to log in to Stack Overflow. Any ideas? Why are Python's 'private' methods not actually private? Where are the save files in Skyrim? I'm exploring the effects of removing the intercept in a logistic regression model.  Assume a model:  $$logit(Y = 1) = \beta_1 x + \beta_2z + 0$$  with $x$ and $z$ being categorical variables with 2 levels each and no intercept.  I understood that having no intercept with categorical predictors produce coefficients that compare the $P(Y = 1)$ in each level of the two predictor against a null case where $P(Y=1) = 0.5$ or $logit(Y=1) = 0$.  I noticed a phenomenon that can understand. Using glm() function in R if you change the order of the variable in the right hand part of the formula, the coefficients change too. But even more oddly, the coefficient of the first variable is always the same.  Here's an R demo:  y &lt;- as.factor(sample(rep(1:2), 30, T)) x &lt;- as.factor(sample(rep(1:2), 30, T)) z &lt;- as.factor(sample(rep(1:2), 30, T))  coef(glm(y ~ x + z - 1, binomial) #        x1         x2         z2  #-0.1764783  0.3260739 -0.1335192  coef(glm(y ~ z + x - 1, binomial)) #        z1         z2         x2  #-0.1764783 -0.3099976  0.5025523    As you can see the first predictors have the same coefficient while the other are different in the two models.  Here is what I expected and instead behave differently than what I though:   Since every level of the two predictors is compared to the same null case, I expected to have the same coefficients in the two models, independently from the order in which I use them. I expected to see the coefficients of every level of every predictor, instead the coefficient for the 1 level of the second predictor is not shown. I therefore assume that only the first variable is compared against the null case, while the second is compared against a reference level; but what is this level? Is it $P(Y = 1 | X = 1 \cap Z = 1)$? Reproducing one of the models WITH the intercept we get:  coef(glm(y ~ x + z - 1, binomial) #        x1         x2         z2  #-0.1764783  0.3260739 -0.1335192  coef(glm(y ~ x + z, binomial)) #(Intercept)         x2          z2  #-0.1764783   0.5025523  -0.1335192    As expected x1 become the intercept, and x2 is likely relative to x1. z1 is missing also in this case and z2 is the same as in the model without intercept.  Thus should I assume that the comparison against the null case $P(Y = 1) = 0.5$ is made only for the first variable in a formula, while the other are compared against the usual intercept? Is this behavior normal? What about the fact that the first coefficient has the same value whichever the order of the predictors in the formula? What if I want to compare all level of each predictor against the null case and have a coefficient for all levels? Or it's theoretically impossible for some reason I don't get? How to scroll in a terminal using keyboard? How can I scroll in bash using only the keyboard? If it's not possible in bash, are there any other shells that support this? Create database fields to an existing table when installing a module I'm new to drupal and I need some help.  I created a new module with name user_extra. Which create necessery table when Installing the module.  But I also need to insert some database field in 'users_field_data' table ('user_extra_id' and 'user_office')  In baseFieldDefinitions I wrote all necessery database table fields for user_extra table.   public static function baseFieldDefinitions(EntityTypeInterface $entity_type) {     // Standard field, used as a unique if primary index.     $fields['id'] = BaseFieldDefinition::create('integer')         -&gt;setLabel(t('Unit ID'))         -&gt;setDescription(t('The unit ID.'))         -&gt;setReadOnly(TRUE)         -&gt;setSetting('unsigned', TRUE);      $fields['uuid'] = BaseFieldDefinition::create('uuid')         -&gt;setLabel(t('UUID'))         -&gt;setDescription(t('The unit UUID.'))         -&gt;setReadOnly(TRUE);         .         .         .     $fields['user_info'] = BaseFieldDefinition::create('string')         -&gt;setLabel(t('User Info'))         -&gt;setDescription(t("The User Info"))         -&gt;setSetting('max_length', 255)         -&gt;setDisplayOptions('form', array(           'type' =&gt; 'string_textfield',           'weight' =&gt; 10,         ))         -&gt;setDisplayConfigurable('form', TRUE);      return $fields;      }   When I install the module it inserts all values that I define in baseFieldDefinitions.  But I also need to create 'user_extra_id' and 'user_office' in 'users_field_data' table with setDisplayOptions and setDisplayConfigurable options.  This is the commenting that I made in entity file  /**  * @ContentEntityType(  *   id = "user_extra",  *   label = @Translation("user extra"),  *   handlers = {  *     "storage" = "Drupal\user_extra\UserextraStorage",  *     "storage_schema" = "Drupal\user_extra\UserextraStorageSchema",  *     "access" = "Drupal\user_extra\UserextraAccessControlHandler",  *     "list_builder" = "Drupal\user_extra\UserextraListBuilder",  *     "view_builder" = "Drupal\user_extra\UserextraViewBuilder",  *     "views_data" = "Drupal\user_extra\UserextraViewsData",  *     "form" = {  *       "default" = "Drupal\user_extra\Form\UserextraForm",  *       "add" = "Drupal\user_extra\Form\UserextraAddForm",  *       "edit" = "Drupal\user_extra\Form\UserextraEditForm",  *       "delete" = "Drupal\user_extra\Form\UserextraDeleteForm",  *     }  *   },  *   admin_permission = "administer user_extra",  *   base_table = "user_extra",  *   entity_keys = {  *     "id" = "id",  *     "label" = "name",  *     "uuid" = "uuid",  *   },  *   links = {  *     "canonical" = "/admin/user_extra/{user_extra}",  *     "add-form" = "/admin/user_extra/add",  *     "delete-form" = "/admin/user_extra/{user_extra}/delete",  *     "overview-form" = "/admin/user_extra/${user_extra}/overview",  *     "edit-form" = "/admin/user_extra/{user_extra}",  *     "collection" = "/admin/user_extra",  *     "children" = "/admin/user_extra/{user_extra}/children",  *   },  * )  */ Let $X$ be a locally compact metric space which is also $\sigma$-compact. Let $C_{c}(X)$ be the continuous functions on $f$ from $X$ to $\mathbb{R}$ with compact support. Is $C_{c}(X)$ separable?  My work so far:   If $X$ is a compact metric space, then by Urysohn's Lemma and Stone-Weierstrass, the continuous functions $C(X)$ on $X$ are separable and hence the result follows as $C_{c}(X) = C(X)$.  Suppose $X = \mathbb{R}$. Write $\mathbb{R} = \bigcup_{N  = 1}^{\infty}[-N, N]$. Let $f \in C_{c}(\mathbb{R})$. Then $f$ is supported on a compact set $K \subset [-N, N]$ for some $N$. Thus $C_{c}(\mathbb{R}) =\bigcup_{N = 1}^{\infty}C([-N, N])$. Each $C([-N, N])$ has a countable dense subset $\{\psi_{N, n}\}_{n = 1}^{\infty}$ and so $\bigcup_{N, n = 1}^{\infty}\{\psi_{N, n}\}$ is a countable dense subset of $C_{c}(\mathbb{R})$.  In the general case, $X = \bigcup_{i = 1}^{\infty}X_{i}$ where each $X_{i}$ is compact and $X_{1} \subset X_{2} \subset \cdots$. Let $f \in C_{c}(X)$. Then $f$ is supported on a compact set $K = \bigcup_{i = 1}^{\infty}K \cap X_{i}$. Is it still true that $C_{c}(X) = \bigcup_{i = 1}^{\infty}C(X_{i})$? I've logged in and out, restarted my phone, updated, but the Pokemon footsteps indicating whats nearby wont show up.   The Pokemon still appear in the menu, but I cannot click to select them, nor does it show their distance from me with the footsteps.   What is going on? How to calculate the integer part of the value of the following equation?  $$y=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\ldots+\frac{1}{\sqrt{1000000}}$$  It should be calculated in a special way, after all the equation is so long. today I installed Ubuntu 64-bit on a netbook. When the netbook boots this, error report appeared. I think there is a problem with the partitions.  Gave up waiting for root device. Common problems:   — Boot args (cat /proc/cmdline)     — Check rootdelay= (did the system wait long enough?)     — Check root= (did the system wait for the right device?)   — Missing modules (cat /proc/modules; ls /dev) ALERT! /dev/mapper/ubuntu--vg-root does not exist. Dropping to a shell!   BusyBox v.1.21.1 (Ubuntu 1:1.21.1-1ubuntu1) built-in shell (ash)    Enter 'help' for list of built-in commands.    (initramfs)   Output of lsblk as requested:  $ lsblk NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 232.9G  0 disk  ├─sda1   8:1    0   231G  0 part  ├─sda2   8:2    0     1K  0 part  └─sda5   8:5    0     2G  0 part [SWAP] sr0     11:0    1   1.2G  0 rom  /cdrom loop0    7:0    0   1.1G  1 loop /rofs Are the off-world colonies really a "golden land of opportunity"? In Blade Runner, there seems to be quite a  for emigration to the off-world colonies, e.g.,      "A new life awaits you in the off-world colonies, a chance to begin   again in a golden land of opportunity and adventure."   Is there any evidence that people emigrating are actually better off than staying on Earth?  The job descriptions of the replicants Deckard is tasked with "retiring" don't seem consistent with the colonies being wonderful places. If the colonies offered a good life, would they have to do so much advertising? Choosing my name as an author when publishing a scientific paper, can I use my "unofficial" first name? I have one official first name which appears on my ID card. I have another first name which friends call me by. Is it possible to use my unofficial first name and official family name to publish scientific papers? How can I prove to someone that I am one of the authors? Where to set proxy ignore list? I upgraded to ubuntu 11.10 from 11.04, shocked to see few things...    My system is behind a proxy, so I did set a proxy setting. Being a web developer, I want to remove a lot of addresses that I type in browser address bar to not hit proxy. There's no such ignore list in ubuntu 11.10, what/where do I do it? What was the requirement to change the way network gui worked?