For sliding MAXIMUM: maintain decreasing queue. Larger elements dominate smaller ones. For sliding MINIMUM: maintain increasing queue. Smaller elements dominate larger ones. For "earliest" queries: maintain strictly monotonic. For "latest" queries: allow equal values.
When in doubt: think about what makes an element "dominated". If A is worse AND older, discard it. The choice depends on whether you want max (decreasing queue) or min (increasing queue).