Category Theory
Zulip Server
Archive

You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.

Stream: learning: questions

Topic: Writing style

Leopold Schlicht (Oct 20 2021 at 17:00):

Which formulation is better:

1. Consider the family $\{k_P\colon FP\to GP\}_P$ of morphisms.

2. Consider the family of morphisms $\{k_P\colon FP\to GP\}_P$.

Nathanael Arkor (Oct 20 2021 at 17:04):

In your example, there's not much difference between the two. But often (1) is preferable. E.g. in the sentence "Consider a category $\mathbf C$ with a distinguished object $X$.", it's awkward to rewrite to place $\mathbf C$ at the end. You could say something like "Consider a category with a distinguished object $(\mathbf C, X \in \mathbf C)$.", though this doesn't read as nicely for me.

Nick Hu (Oct 20 2021 at 17:11):

I think the second is better, because it avoids splitting up 'family of morphisms'. If I read the first, I might read 'family' and then the set and think 'family of what?', until reading the end of the sentence

Ralph Sarkis (Oct 20 2021 at 17:11):

I am not a native speaker, but 2 sounds better to me in this case. I believe 1 is better in cases where you specify what kind of morphisms you are talking about, i.e.: consider the family $\{k_P : FP \to GP\}_P$ of morphisms that (e.g.) are in the image of $U$. However, 2 can also be better if you want to add precisions to the family, i.e.: consider the family of morphisms $\{k_P:FP \to GP\}_P$ that (e.g.) is of cardinality $\kappa$.

John Baez (Oct 22 2021 at 18:07):

I am a native speaker but 2 sounds better to me. But these issues are a bit subtle; for example I also agree with Nathaniel that

"Consider a category C with a distinguished object X"

sounds infinitely better than

"Consider a category with distinguished object X, C."

or even the less terrible alternative he mentioned.

Mike Shulman (Oct 22 2021 at 18:10):

I don't think "consider a category C with a distinguished object X" is an instance of 2. Here "a category" is a sufficient description of what C is, and then afterwards we also consider a distinguished object X of C. By contrast, in the OP question, "the family" is not a sufficient description of what $\{k_P\colon FP\to GP\}_P$ is; what it is (all on its own) is "a family of morphisms".

John Baez (Oct 22 2021 at 18:14):

Yeah, it's too complicated for me: "category with distinguished object" is a reasonable kind of thing to consider, like "pointed set", but "category with distinguished object X" is not a reasonable kind of thing to consider: you never wake up and say "I want to prove a theorem about a category with a distinguished object called X".

John Baez (Oct 22 2021 at 18:15):

I just know how to write fairly well; I can't really explain the theory of how to do it.

Tim Hosgood (Oct 23 2021 at 14:37):

i think about this exact problem quite a lot, and, to give a different answer from the consensus here, these days i opt to write something like “consider the family $\{k_P\}_P$ of morphisms $FP\to GP$”

Tim Hosgood (Oct 23 2021 at 14:37):

i’m not saying that this is a particularly good way of writing it, but it’s what i’ve settled on

Tim Hosgood (Oct 23 2021 at 14:37):

or something similar, basically merging 1 and 2