What does き stand for in 招き猫?


As question suggests: what does き stands for in 招き猫? Is it some sort of
particle, that "connects" 招(invitation) and 猫(cat) or something else?




No, き here is a part of the 招き - invitation. It's an okurigana, you can say
that it's a reading hint to know that 招 should be read using a _kun_ reading -
まねき and not an _on_ reading - しょう.

