With, I hope, more consideration to the reader than Humpty Dumpty I ask the
reader to associate some particular meanings with certain words; though I
discuss the nature of relationships among values in general terms, I abstract
from that discussion very specific meanings for the type
relation and the
relate. Within the universe so carved out, various types of
relation emerge, as do various particular relations; some of these are of such
significance as to deserve names, which I'll endeavour to document in this
directory. I do try to chose names which are compatible with orthodox and
vernacular meanings of the words used, but orthodoxy and the vernatular aren't
always compatible, and sometimes no word presents itself for the task in hand;
hence the need to document my exact intent in a glossary.
Some of entities thus named are characterised by certain core properties that may be realised in diverse specific ways. Each such realisation is, for the purposes of the entity's general specification, equivalent; yet each may have incidental properties (implementation details) peculiar to itself, compatible with but not demanded by the core properties that characterise the entity. A common practice in mathematical writing is to use the abstract form of such an entity, treating each realisation as an image of it under some isomorphism and stripping the named entity of all incidental properties. This has the virtue of ensuring that each writer's discourse says nothing about the named entity that isn't also true in other writings. However, where I see a particular realisation of such an abstract entity that has incidental properties I find useful, I have chosen to use that particular realisation as the entity so named; this enables me to exploit its implementation details as a way to specify the abstract entity's interaction with other things. I take some care in chosing these particular realisations; and aim to document, in bestiaries, which ones I have chosen for each abstract specification.
The denotations used in the bestiaries and glossaries below, I document elsewhere: if something with lots of punctuation in it, and/or a ←, confuses you, it's probably a denotation for a relation; likewise, if confused by pieces of italic text (and punctuation), especially if interspersed with bold text and no ordinary-font text, the odds are good you're looking at a template. As matters stabilise, I'll aim to have each entry reference the discourse which introduces it more fully elsewhere; and to use the entries here as the route via which links from other pages using the relevant jargon will reach such primary discussions. This may take some time, though (2001/July/8, still true 2015/May/30).