Added an entry for *sieve*: here.

]]>A

sieveis just a subfunctor of a representable functor, but calling them “sieves” serves to indicate that (mostly) one is interested in regarding these ascoversof a Grothendieck topology or coverage, making the ambient category into a site.

added one more item: lists:

A *list* is just a tuple, but calling it a list indicates that one is interested in the operation of concatenation of lists.

Finally following up on #30 I have moved a couple of the less compelling examples to the end of the entry, under “Further examples” (now here).

While at it, I adjusted and then expanded wording of the the previously incomplete example “Module objects” (now here).

]]>Added (here) one more item to the list:

An *abstract re-writing system* is just a relation on some set $X$.

However, calling this relation an abstract rewriting system indicates that one is interested in studying the behaviour of chains of related elements $x \to x_1 \to x_2 \to \cdots$ (thought of as successive stages of rewriting $x$), for instance to see if they are confluent.

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Yeah I get what you mean. In certain foundations of set theory such as ETCS, an “element” is also a concept with an attitude, being simply a function out of the terminal set, which is not the case in other foundations of set theory (SEAR, MLTT, etc).

]]>Thanks.

Somehow *subset* is not quite as satisfying an example. The good examples would have lay people say: *What do you mean by X? Ah you just mean a Y.* This is not so plausible for X = subset and Y = predicate.

Of course I see what you mean. Maybe we should bring some order into the list, having the more striking examples be on top and the more subtle ones further below.

]]>added subsets

Anonymous

]]>Added curves from differential geometry

Anonymous

]]>adding dynamical systems

Anonymous

]]>added (here) an item for *persistence module*

Thanks. That Young diagram was over-ambitious.

]]>Made it singular, tableau.

]]>added this example:

A *Young diagram* is a partition that wants to become a Young tableau.

Added copresheaf.

]]>I added series as an example. I put it first since it’s the most elementary and hence the easiest to understand.

]]>Sure, I like that example. Please add it.

]]>Would ’sequence’ and ’series’ be an example?

A *series* is just a sequence. But one says *series* instead of *sequence* when one is interested in studying partial summations.

Or would that be stronger than ’with an attitude’ because the word ’converges’ means different things? The series $n\mapsto a_n$ converges if and only if the sequence $n\mapsto \sum_{i\lt n}a_i$ converges, which is different from the sequence $n\mapsto a_n$ converging.

]]>Added one more example (here):

Tensor networks in solid state physics are string diagrams with an attitude.

]]>Adjusted accordingly.

]]>To keep it fun, I suggest to make sure that each item in the list starts out with the exact same pattern, with the words: “An X is just a Y. But one says ’X’ in order to…”

]]>To be honest, this sort of thing often annoys me. Why would you choose to create confusion by introducing a new word that has the same meaning as an old word, just because you’re going to do something new with it?

I would say that often the situation is more complex than that. In two situations you may end up with the same (or equivalent in some sense) object, but what you want to express is different and it should perhaps be viewed as a lack of the formal definition that it does only incompletely cover what you want to say, e.g. the definition of an estimator actually should contain also some information about the model in which the estimated parameter lives.

Another point is that sometimes a systematic terminology can not be tailored with respect two two different areas of application, e.g. the term presheaf makes sense in sheaf theory, wheres contravariant functor makes sense in category theory.

]]>Added what is in my impression “the king of examples” (at least with respect to the overall mathematical community), random variables and estimators.

]]>Jon Beardsly indavertendly prodded me (here) to add one more item to the list of “concepts with an attitude”:

]]>A

field (in physics)is just a section of a fiber bundle.But…

Re #11: Just to play the devil’s advocate, I would have to look up what “singleton pretopology” means, whereas I understand immediately what the longer sentence means :-).

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