J connects prepositions to their objects.

	     +-Mp+----J---+    +-----MVp----+-J-+
             |   |        |    |            |   |
	The man with the hat chased the dog on Tuesday

Proper and common nouns, accusative pronouns, and other words
that can act as noun-phrases have "J-" disjoined with their
S+, SI-, and O- connectors.

Prepositions have "J+ & (Mp- or MVp-)". "Mp" is used for
prepositions modifying nouns; "MVp" is used for prepositions
modifying verbs and adjectives.  Prepositions may also have
other connectors, disjoined with J+, such as Mg+, Mv+, and
QI+; see "MV: Other Uses of MVp and MVs".

Jw is used to connect prepositions to noun-phrase
question-words in the construction "To whom were you
speaking?"  The construction formed here is very similar to
that formed for determiner-question-words, as in "To which
person were you speaking?" See "JQ" for an explanation. Jw is
also used in prepositional relative clauses, like "The room IN
WHICH I was working was cold". See "Mj".

Regarding Jr, see "B: Noun-Modifying Prepositional-Object
Relative Clauses". Jm and Jy relate to comparatives;
see "MV: Comparatives", sections II (Jm) and VII (Jy).