Do not put an unopened (still quality-sealed) plastic-lidded, plastic jar of mayonnaise in the refrigerator. It is shelf-stable until opened and does not require said refrigeration until after you break the seal, and putting it in the fridge before the seal is broken will only cause it to contract and seal even more tightly, making it impossible to open without super-human strength and necessitating running the lid under warm water to warm it up (not the happiest thing to have to do to a jar of mayo) before you can open it for your two year old who is screeching at the top of her lungs, "May-nays! Want may-nays bread kheese!" and getting underfoot as you try to open it to spread it on her bread and make her a cheese sandwich.
(Hear that, Jeff?)