• Kate here is doubled with Kate Strong. From GlasheenThird Census, (“Strong, Kate”):

Chart (q.v.) says: ‘The most odious of Dublin tax collectors . . . a woman, Kate Strong. The peolpe erected an effigy of her, armed with a toll-dish of utterly unfair proportions.’ Fitzpatrick (q.v.) says: ‘Katherine Strong, a widow, in herited from her deceased husband the post of city scavenger, and a grant of tolls for performing the duties of that office. The lady . . . seems to have been much more active in collecting her dues than in removing the abundnt filth of the city, notwithstanding the oath the city scavengers were bound to take.’ (ellipses hers)

That Kate Strong is a scavenger, and that Kate the Cleaner dumps the family refuse, links them both to the middenheap where Biddy the Hen finds the letter, which is also to say links the same name, “Kate,” to the letter both as the person who dumped it in the middenheap with the refuse and the person who finds it. Though, I think that is a linking of opposites (a la Bruno and the coincidentia oppositorum). Kate the Cleaner is not the person who finds the letter, Biddy the Hen is. (Whether Biddy the Hen is literally a hen is another question.) In the same line, the two are linked with ALP as the River Liffey, which is poluted with the garbage of Dublin.

Kate Strong appears later in the trial:

Kate Strong, a widow (Tiptip!) – she pulls a lane picture for us, in a dreariodreama setting, glowing and very vidual, of old dumplan as she nosed it, a homelike cottage of elvanstone with droppings of biddies, stinkend pusshies, moggies' duggies, rotten witchawubbles, festering rubbages and beggars' bullets, if not worse, sending salmofarious germs in gleefully through the smithereen panes – Widow Strong, then, as her weaker had turned him to the wall (Tiptiptip!), did most all the scavenging from good King Hamlaugh's gulden dayne though her lean besom cleaned but sparingly [. . .] (79.27-36)

(Note the “Tip”s seen in the Museyroom.)

 

• This last sentence is echoed in the trial as well:

And so it all ended. Artha kama dharma moksa. Ask Kavya for the kay. And so everybody heard their plaint and all listened to their plause. The letter! The litter! And the soother the bitther! (93.22-23)

• The context, in the literal-narrative sense, is a tour through a museum dedicated to Wellington: the Battle of Waterloo in particular and his career in general. But in another context, one level of metaphoricity back, the scene is that of a bedroom, with pointers to the HCE/ALP bedroom in particular (as well as to future scenes in the book). As such, the scene has a second literal-narrative context, though one that appears before its time: Kate the Cleaner is telling tales out of school, as it were, gossiping about the sex life of Humphrey and Anna. In that the battle/combat themes here are overwhelmingly metaphors for sex, the episide fits within a third, mythic context, that of the hierophanic and of the nature of the mythic feminine principle.

Conflict is inherent to ALP, which is expected in that she is the incarnation of the feminine archetype (animus). Plurabelle is, in fact, derived from a phrase oft repeated in the Wake, associated with ALP: “pia et pura bella.” The Latin has two meanings: “pious and pure pretty [woman]” and “pious and pure wars.” Benstock more than once refers to Anna as engendering the conflicts between the males (if not conflict in general), which would also go with ALP as the feminine principle.

From the Classical LexiconO Hehir and Dillon, Classical Lexicon of the Wake, 623:

bella, pia et pura The ambiguity afforded by the L word bella yields Joyce endless confusion in Finnegans Wake. As a noun, it is plural of neuter bellum, "war"—i.e., it means "wars." As a feminine singular adjective it means "pretty" or "nice." In conjunction with the name of Anna Livia and the feminine singular adjectives pura and pia, bella would seem to form part of a string of attributes of the Blessed Virgin, or a woman like her pia, pura, bella: "dutiful, chaste, fair." Ancient etymologists responded to this ambiguity by deriving bellum, "war," from bella (feminine), "nice," by the process kaf antiphrasin ("according to the opposite"): "bellum, quod res bella non sit" – "war (bellum), because it would not be a nice (bella) thing." But Joyce's source for the manifold uses of the phrase is not a pious medieval formula, rather it is Vico's prescription for the establishment of civilized hierarchical society: pia et pura bella, "pious and pure wars." As usual, he is able to make words contradict themselves.

This for me goes even more to how the Museyroom is ALP’s womb; but I admit a great metaphoricity there: “womb” being read as the chaos of the feminine waters of creation.