OK. A single object that is singular is it’s own category.
an object is a collection of properties.
properties could be musical notes played on a stringed instrument.
A collection of musical notes played at the same time might be a chord.
if something resonates in the room the same as the musical instrument and it is playing the same chord, then the singular object in its own category might gain a second member.
“associated with” by virtue of resonance.
this is parallel. objects are parallel. properties are parallel. chords are parallel.
but a category is serial within itself. it must be so it can contain countable members. a category parallel too but it’s internal structure is serial.