I don't quite understand what does equal mean for morphisms in category theory. Since object of a category is not necessarily a collection of some elements, then how to decide whether two morphisms are the same or not? Is it allowed that for some category $C$, there exist two different morphisms $f,g$, but for any possible  h which is not a identity morphism, $f\circ h = g\circ h$ and $h\circ f = h\circ g$ (so that there does not exist any monic or epi morphisms in this category, and any objects $a$ of this category do not have any structure such as $x \in a$)? Or we can never know it?
I am learning basics of the category theory (CT).  I do understand that CT is a modern powerful framework to describe various branches of mathematics in a unified way.  I do admit that category's definition tells a lot about the whole thing and focuses on the most important properties, shadowing unnecessary details. However, the more I go forward, the more it feels like it should explicitly require a notion of morphisms equality (like it does with morphism composition). It feels so because equality or inequality of morphisms arises everywhere, since the very beginning: any commutative diagram eventually reduces to an equality of two different paths and many other things involve equality as well. Even composition is defined grounding upon an (implicit) equality!  I'll try to give an example of my concern. Consider $\mathbb{SET}$. Its objects are sets and morphisms are functions. Now, let's recall that functions are sets as well - to be more precise, a function $f : A \mapsto B$ is a subset of a $A \times B$ obeying certain properties, which I omit. Thus, one could argue that $f$ is both a morphism between objects $A, B \in Obj(\mathbb{SET})$ and an object defined as a set of pairs $\{ (a_1 \in A, b_1 \in B), ..., (a_n \in A, b_n \in B) \}$ and those are equal because both are essentially exactly the same thing.  I hope my concern is clear and I need some kind of "conceptual insight" from knowledgeable people to move forward. Please give me the right perspective.
How to tell what method was used to log in (Password vs. Keyfile) from the bashrc Is there a way how you can check what auth method the user which just logged in to an account were using?  I like to print out a warning after login if someone is using a password instead of a keyfile.  Sure one solution is to check the ssh-logs. But is there a nicer way to do this? Since looking up logs could impact performance depending on the log size and method you use to gather this information.  We are using SUSE and Ubuntu. How do I make Bash my default shell on Ubuntu? Adjective meaning "argumentative for argument's sake"? parskip package, keep the indents That may be a stupid question but is there a way to keep the indent while using the parskip package? I use parskip to keep spacing between my paragraphs while leaving the table of contents and lists intacts but I would like to keep the indents in my text.  Code 1 :  \usepackage{parskip}  \tableofcontents  \section{Section 1} \subsection{Sub 1}  Paragraph 1  Paragraph 2   Code 2  \setlength{\parskip}{10pt}  \tableofcontents  \section{Section 1} \subsection{Sub 1}  Paragraph 1  Paragraph 2   Basically I want the aspect of the table of contents (and possible lists) from the code 1 while keeping the indent like in the code 2. The package parskip works great but I just don't like that it deletes the indents and I'd like to find a way to prevent it from doing that.   Thank you. Spanning volume disk usage I have two SSD disks of 256GB and I want to create a single spanning volume of 512GB. I am using Windows 10. What I want to know is how will Windows handle this under the hood.  Will the first disk fill up before the second one starts being used, or will Windows use both disks. For example, if I have 256GB of data on the spanning volume, will it be divided to 128GB on first and 128GB on second physical disk or will it all be on the first disk with the second disk empty? Would this behavior be any different if I were using two HDDs? What do "watched tags" and "ignored tags" do? URL regex passed by regex buddy but failed by Dart How to pluralize an acronym which ends in 'S' correctly? When using the acronym package, how can you  an acronym which ends on 'S'?  Take the acronym: OS - operating system  It should be pluralized as OS's, but is pluralized as OSs when using \acp. The well-known fable of an astronaut sending signals out to an external observer while falling toward an event horizon states that the time lapse between such signals becomes greater even if in the astronaut sends them out periodically (as judged in his inertial frame). When viewed from earth and weighing time-dilation due to the gravitational field of the collapsing star, how is it possible that a black hole can form in finite time (for any external observer) if it takes an infinite amount of time to "see" events occurring at the event horizon? Permanent PATH variable How will I make this /media/De Soft/mongodb/bin PATH variable permanent?  Everyone is saying "export PATH=$PATH:media/De\ Soft/mongodb/bin to your ~/.profile, or .bashrc, or .zshenv depending on your shell".   I don't know what is ~/.profile, or .bashrc, or .zshenv. What do they do actually?  How will I add export PATH=$PATH:my/path to my .profile/.bashrc/.zshenv?   I'm using 64 bit Ubuntu 14.04 LTS with default terminal. Webform redirect I'd like to do something pretty straightforward: After user fills out a , I'd like a button that simply redirects them to a URL (in this case it's to a demo sandbox). Of course I'd want the user to fill in their info to capture for lead-generation purposes. My  is set up correctly in that it correctly captures all the user fields and submits them to me via email. However, upon completion "click" I'd like to have the user redirected to a determined internal URL www.mysite.com/foo  I can't figure out how this is done with the vanilla webform settings. Am I missing something obvious? Let $f: B(0,1) \rightarrow \mathbb{C}$ be holomorphic and suppose $\exists\ r \in (0,1)$ such that $f$ is injective in $A = \{z \in \mathbb{C} : r &lt; |z| &lt; 1\}$. Prove that $f$ is injective.  I tried using Rouché theorem, or the identity theorem, but I don't know what to do. Any hints? :) I'm writing a bash script that needs to delete old files.  It's currently implemented using :  find $LOCATION -name $REQUIRED_FILES -type f -mtime +1 -delete   This will delete of the files older than 1 day.  However, what if I need a finer resolution that 1 day, say like 6 hours old? Is there a nice clean way to do it, like there is using find and -mtime? About Trivariate Normal Distribution I am working on a paper, and have a problem regarding ellipsoid and Trivariate Normal Distribution. Suprisingly I can't find much in literature but I found your in one of your answers:     Because this construction has nothing to do with "confidence" per se,   the objective is to establish some convention for describing the shape   and relative size of the points. Using 1.96 sort of works (for three   variables): it contains about 72% of the probability of the trivariate   normal distribution. But as the number of variables increases this   method produces ellipses that are far too small. For instance, with 10   variables it will contain only 4.6% of the probability; using 4.28   instead of 1.96 in this case will contain 95% of the probability.   How did you get this number 72%? Or do you have some literature to recommend to me in which I can find this. I would appreciate it very much! Select Input Texture file name as parameter/node I am trying to create a material node group for triplanar mapping, but I am not sure how I can parameterize the image texture name.   I have 3 image texture nodes, which all use the same file with the same settings, the only difference is the vector input.  Is there a way I can make it so that I only have to select the texture name once, possibly as a input for a group? Link to the recommended job is broken in the mobile apps The link to the recommended job in the app brings you to a page with the text: Not Found    Looking at the link it seems like after changing the URL structure in Stack Overflow Jobs they have not been updated in the apps.  For the job in the screenshot this is the used URL in the app:    The correct URL is: Natbib -- change author conjunction in citation call-out from 'and' to '&' I'm using natbib, german babel and natbib creates output of the form   Foo and Bar (1337)   I would like to get   Foo &amp; Bar (1337) for citet and (Foo &amp; Bar 1337) respectively for citep. Is it possible to check a bash script syntax without executing it?  Using Perl, I can run perl -c 'script name'. Is there any equivalent command for bash scripts? Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$ How can I calculate the integral $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$ by substituting $t=\frac{1-x}{1+x}$. Command line move file with long directory path without repeating directory path Is there any way of executing a mv command without typing the full path in the second argument?  Example:  mv my/file/that/has/a/really/long/path/foo.bar some_magic_operator_that_means_the_same_directory/foo.baz