Check the local auto parts store, or a car stereo and alarm shop. They have remote kits designed for retrofit installation. Some are designed specifically for door locks; some just turn a relay on and off. The kit will come with a key fob transmitter, a receiver that runs on +12 V DC, and possibly some relays and lock motors.
If the relays are external to the receiver, the receiver output(s) will probably be designed to switch +12 V at 200 mA or so to a relay coil - the "standard" automotive relay coil pulls around 150 mA.
Keep in mind that the receiver will draw a small amount of current all the time, which may not be what you want if you're using a battery at the shed. Depending on how much the receiver draws, it might not be a crazy idea to use a stack of alkaline D cells or something like that just to run the receiver.
A couple of examples follow. I don't know if these are any good or not, just that they exist. You can probably find a greater selection at a car stereo and alarm shop.
1 channel, internal relays for 6 A:
4 channels, internal relays for 6 A:
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