[Tex/LaTex] For Hom and H*(X,Z) — which fonts?

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This is a question about style, I am debating whether the math operator \Hom should be just

\DeclareMathOperator{\Hom}{Hom}

or if it should be some variant like

\DeclareMathOperator{\Hom}{\mathnormal{Hom}}

The reason I'm even considering this is because I'm using the eulervm package. Also, when I write something like cohomology $H^*(X,Z)$, I do not use \text{H} but leave eulervm's mathematical font.

What do you think? Does the question make sense?

Here is a minimal example with the two choices.

\documentclass{amsart}
\usepackage{eulervm}
\begin{document}
\[ \operatorname{Hom}(A,B) = 0 \]
\[ \mathnormal{Hom}(A,B) = 0 \]
\[ H^2(X,Z) = 0\]
\[ \operatorname{H}^2(X,Z) = 0\]
\end{document}

Answer 1

Both “Hom” and ”H” are similar to “log”, so they should be typeset in the text font (upright). However it's not a sin to have different opinions.

The most important thing is that you use macro definitions:

\DeclareMathOperator{\Hom}{Hom}% preferred
%\DeclareMathOperator{\Hom}{\mathnormal{Hom}}% with Euler type
\DeclareMathOperator{\HH}{H}% preferred
%\DeclareMathOperator{\HH}{\mathnormal{H}}% with Euler type

Not \H, because it's already reserved.

In the body of the document you'll use only \Hom and \HH. This way, you can delay the choice to the last moment.

Tightening the space in “Hom” in Euler type is not a choice: look at the following picture to see why.

Here's the source for the image

\documentclass{amsart}
\usepackage{eulervm}
\begin{document}

\newcommand{\test}[1]{$H\mkern-#1mu o\mkern-#1mu m$\par}

\test{0}\test{0.2}\test{0.4}\test{0.6}\test{0.8}\test{1}

\end{document}