When Deputy Chief Brenda Leigh Johnson moves into a new house in season one (two?), she discovers a cat that has been living in the home already, whom she names "Kitty".
"Kitty" is a she, but Brenda keeps referring to her pet as a "he," despite being constantly corrected by her significant other. While her initial ambivalence towards the cat changes, this incorrect gender identification does not.
In the beginning of season five, the cat passes away. She grieves and carries the cat's ashes around with her, first as a mistake, and then as a remembrance. The ashes are finally placed on the mantle in a fancy urn, despite Brenda's opposition to such practices earlier.
In literature, cats carry a symbolic value, for things like cleanliness and good fortune (see Wikipedia). It seems as though for being such a minor "character" this cat gets a lot of attention in the series to not mean something to the plot or character development.
Is there a deeper connection between Brenda and the cat that the writers and director are trying to establish? Are they comparing Brenda's strong skills in interrogation to "catching a rat"? If she's so close with the cat, why does she maintain this distance with the name "Kitty" and referring to she as a "he"? (drawing on any hints from official sources or evaluations from critics if possible)