[goto11]

Pet peeve: The word "just" when used to gloss over something with the author don't know how to explain. Using "just" shift the burden from the author to the reader, since it signals it is the readers fault if they don't understand.

> A homomorphism is just a structure preserving map. In fact, a functor is just a homomorphism between categories as it preserves the original category's structure under the mapping.

How about removing the "just":

> A homomorphism is a structure preserving map. A functor is a homomorphism between categories as it preserves the original category's structure under the mapping.

Much clearer. Although most readers would now ask what "structure" and "structure preserving" means, since this is never explained.

[saithound]

Mathematicians use "just" with a specific meaning: it is not used to gloss over something that the author doesn't know how to explain. It has a purpose, useful for mathematically trained readers.

For suc a reader, "a homomorphism is just a structure preserving map" makes it clear that "homomorphism" and "structure-preserving map" can be used interchangably, and that by understanding one of the concepts, you'll immediately understand the other as well.

When you got rid of the word "just", you got rid of this connotation and changed the meaning of the sentences.

E.g. the sentence "a functional is a linear transformation" is correct; but not all linear maps are functionals, so writing "a functional is just a linear transformation" would be plain wrong in a mathematical setting.

[lachenmayer]

That would be an extremely good thing to explain in the introduction. I feel like this kind of very culturally-specific usage of everyday words is what makes math/CS papers so impenetrable for many people.

The word "easy" is another example: saying "it is easy to show X" (just?) means that X can be derived from the already stated theorems in a more-or-less mechanical way without having to introduce new concepts. It does not in any way suggest that deriving this will be "easy" for a student reading the paper.

(Of course the most challenging "easy" parts are best left as an exercise for the reader anyway...)

[jasode]

>Mathematicians use "just" with a specific meaning: it is not used to gloss over something that the author doesn't know how to explain. It has a purpose, useful for mathematically trained readers.

Based on the author's public profile, I'm not convinced the author is a mathematician writing "... is just ..." as rigorous formalizations for a math-trained audience.

Instead, the "is just" phrases are innocently slipping into explanations as a subconscious verbal tic caused by the The Curse of Knowledge. My previous comment on that phenomenon: https://news.ycombinator.com/item?id=28256522

(Also, as a sidebar followup to your comment, Wikipedia's page about homomorphism (https://en.wikipedia.org/wiki/Homomorphism) has this as the first sentence: "In algebra, a homomorphism is a structure-preserving map ..."

I'm guessing that a hypothetical edit to "a homomorphism is _just_ a structure-preserving map" -- in an attempt to add more refinement and precision to the definition... would be rejected and reverted back by other mathematicians.)

[plasticchris]

Sure, but the title does say plain English so this would be the sort of thing the author is trying to avoid. If that’s the meaning just write all a are b.

[saithound]

While I agree that the English used in the repo could be plainer, that's not remotely the same thing as "using 'just' to gloss over something that the author doesn't know how to explain", which was the complaint that goto11 made.

[minraws]

This has not been true in my experience, as someone who is used to talking to a mathematician during my academic life (a bit). They prefer to not use words like "just X".

They generally reply in definite statements, "this is undecidable", "this is an example of X", "this can't be done without Y", they rarely say. "X is just Y", they would probably say, "X is Y".

The "just" implies some form of detail that might be missing in the relation generally. Even my mathematical text books of pretty advanced topics rarely used "just".

Again, what you say is most likely true when math people talk amongst themselves but I don't think they do so with other non math people. I was in compsci.

[mjburgess]

"just" is used across technical academia (including philosophy) to mean "nothing over and above"

[8note]

I don't understand who the audience for this glossary is.

Math students coming from another discipline?

Only some people will understand the technical meaning of "just" as intended

[nabla9]

Both you and goto11 make a good point.

What is needed is "Mathematical English in plain English."

[Akronymus]

I think for the layperson "equivalent to" would work better than "just".

[bjarneh]

> The word "just" when used to gloss over something with the author don't know how to explain.

Never thought of that before, but it's certainly true. Always hated when we got cryptic explanations for the difficult things, and elaborate explanations for the stuff everyone understood anyway at the university. I guess professors have to explain things they don't fully understand from time to time

[mjburgess]

The former means: all Hs are SMPs ; the latter may also mean: some Hs are SMPs.

The former is clearer. Adjust your understanding of `just`, it's definition 4a at https://www.britannica.com/dictionary/just

[josu]

Be the change you want to see in the world haha

https://github.com/hemanth/functional-programming-jargon/pul...

[marcosdumay]

As a hint, any time you read "just" in mathematics, replace it with "exactly". That may make it clearer.

[cinntaile]

This is left as an exercise to the reader.

[minraws]

Just to be clear, that's quite literally the Wikipedia definition.

> In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).

Not sure if this is rude but many definitions there seem a bit, not plain English.

I am assuming we are aiming for something close to ELI5 if the title says plain English.

Ofc that could not be what the author intended and is just but that's how inferred the title.

I will see if I can find time to improve and send some PRs for the ones that are in deep need of simplification, hopefully OP is open to discussing changes.

Also like Arity, Arity is not just for functions, it can sometimes be interchanged with Rank and apply to even Types. higher ranked types. higher arity types... I do understand they are not something most people like, because of their issues but that's not a complete definition so I assumed it was for the means of simplifying to explain to beginner programmers. [reference to issues with HRTs](https://www.sciencedirect.com/science/article/pii/S016800729...)

Again this is not meant to be rude to the author, just hopefully the title could be better formed to explain the intent of the work. Or my opinion might be minority and we can decide against it as well ofc.