Yes, you can absolutely bring a Yeti tumbler, bottle, or mug in your carry-on luggage, provided it is empty when you go through the security checkpoint. The TSA and international security agencies treat Yeti drinkware exactly like any other reusable water bottle or thermos. The stainless steel construction does not pose a security problem, though the thick walls might occasionally trigger an "additional screening" or a manual bag check if the X-ray operator cannot see through it clearly. To ensure a smooth process, place your empty Yeti in a bin or at the top of your bag so it is easily accessible. Once you are past the security screening, you can refill it at a water station or coffee shop. Note that "soft-sided" Yeti coolers are also generally allowed as carry-ons if they fit within the airline's size dimensions, but hard-sided coolers must usually be checked due to their bulk. Just remember: the "liquid" is the restricted part, not the container itself.