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2021-11-18

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**Iu2019ve just started learning how to code. How do simple lines of codes turn into complex websites/apps?**

Through composition.Lines become functions become classes, modules, applications. This creates many interdependencies at different levels which can be alleviated through good design principles such as separation of concerns.Complex applications do not just happen, they grow over time. One of the challenges is effective organisation throughout that growth

**Why is it possible to create loadable kernel modules using a high-level language such as C?**

Most of the popular operating systems are written in C and loadable modules are not really distinct items. The modules are part of the OS and often make calls directly into OS code so must be written to fit in and this is easiest if you use the same language as the base OS. All that really happens when you load a module is that it is run-time linking it into the kernel code, which is why faults in modules can crash the kernel. You can of course code a module in assembler, but you must ensure that the code exactly matches C-calling conventions or the system will just crash.If the system is microkernel based then it may be easier to use other languages as these use a more system-call like architecture for "drivers" to use kernel services

**Can I use fewer modules for implementing my newsletter?**

The MailChimp module is very minimalist, giving you a very good ecosystem !You call sync all your leads (users) to a normal mailchimplist.Here's a tutorial: How-To Article: MailChimp Module for Drupal

**The Modules over Algebras over Operads are not what they seem.**

Yes, a "module over an algebra over $mathttAss$" is indeed a bimodule over that associative algebra. There are plenty of ways to see this, you can find this statement in Loday and Vallette ' Algebraic Operads (an excellent book if you are interested in operads for that matter). Another way to see this is to look at the universal enveloping algebra of an algebra $A$ over $mathttAss$, which is $U_mathttAss(A) = A otimes A^op$ (and left modules over this are indeed $(A,A)$-bimodules).Besides, it's not really surprising - why would the left side be prioritized over the right side? There's nothing asymmetric in the definitions, either in the definitions of the operad $mathttAss$ or in the definition of modules over an algebra over an operad.*It is actually possible to recover left modules over $A$, but the theory is a bit ad-hoc (by this I mean that "left modules" is not canonically associated to the associative operad like "modules" are associated to every operad). I've seen it in Horel's "Operads, modules and topological field theories", Section 3. Given an operad $mathttP$, consider an associative algebra $mathttM$ in the category of right $mathttP$-modules. Then one can define "$mathttM$-shaped $mathttP$-modules" from this data (they are actually a "relative" or "Swiss-cheese type" operad).If you take the enveloping operad $mathttP[cdot]$ (see Fresse's Modules over Operads and Functors for example), then you recover the classical notion of a module over an algebra over an operad, and $mathttAss[cdot]$-shaped $mathttAss$-modules are bimodules over an associative algebra. But it's also possible to define an algebra $mathttAss^$ in right $mathttAss$-modules, such that you get left modules over an associative algebra in this case.One of the main interests of modules over an algebra over an operad is that you can define a (co)homology theory that takes an algebra $A$ over $mathttP$, a module over $A$ and spits out $H_*^mathttP(A;M)$, so in this way if you are looking at things from an operadic viewpoint, then bimodules over associative algebras is the natural thing to consider.* I now realize that in the definition of May you quoted, the $M$ is always on the right-most end. It's actually a trick to save space; there is one such map for every position of $m in M$. So if you are working in an algebraic context, for $p in mathttP(n)$, $a_1, dots, a_n-1 in A$, a and $m in M$, then to define a module structure you need to define $p(a_1, dots, a_i, m, a_i1, dots, a_n-1)$ for all $0 le i le n-1$. In other words, there are $n$ different maps of the type: $$mathttP(n) otimes A^otimes (n-1) otimes M to M,$$ one for each position in which to plug in $M$. It's made more explicit in 12.3.1 of Algebraic Operads.

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