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If you use James Cranch's suggestion, namely to say that the image is a subcategory of $D$, you should make sure that it's actually true in your situation, because it might not be in general. $B$ mig …

"Urelement" is used in set theory as a fancy name for an atom, i.e., something that can be a member of a set but is not itself a set.

Unfortunately, the same terminology is also used with other meanings. For example, in probability theory, "characteristic function" often means the Fourier transform of a probability distribution. …

Many examples can be obtained by the following scheme: Let $x$ assign to each pair $(p,q)$ in $S$ either the fixed element $z_X$ if $p=q$, or, if $p\neq q$, some entity that encodes the distance $d(p, …

I have always assumed that the motivation was more or less as follows. Consider, for example, the projective planes over various fields $k$ (in the sense of classical, long-before-Grothendieck geomet …

Intuitionists use the name "bar" for what you called a blocking set. The relevant context is "bar induction," the principle saying that, if (1) a property has been proved for all elements of a bar an …

The following seems to be sort of a reversed version of Joel's example, categorical in uncountable cardinals rather than in $\aleph_0$. I'll use the theory of the set $\mathbb Z$ of integers with only …

As indicated by Feferman, the key distinction is between two sorts of arithmetical definitions of certain concepts (like "being the Gödel number of a theorem of a given theory"). Suppose I have some …

How about "$D$-class"?

This isn't an answer but it's too long for a comment. I suggest that $n-1$ is more important than $n$ in this context, for the following reason. Suppose $A$ is an $n$-group in a semigroup $S$. Then, f …

This should perhaps be a comment on the answer by Peter LeFanu Lumsdaine, but it's too long and might be relevant in connection with other answers as well. Long ago, Bruce Sagan and I wrote a paper, …