Can we concentrate the "cold of the sky" with a parabolic dish to cool things down during the day? It's well known that we can focus sunlight with a parabolic dish to collect heat. But if we look at the thermal images of the sky we can see that the clear blue sky is quite cool. So by turning the parabolic dish to a clear blue part of the sky, can we exploit its coldness to cool down the object at the focus?
 A: Not exactly a parabolic dish method, but it is possible to cool things this way. The Persians used to make ice for sherbet even in the hot summer by filling shallow pans with water and leaving them out on clear  nights. The water would freeze even though the ambient air temperature was never below freezing.  See Nocturnal ice making in Early India and Iran. 
A: Coldness is not radiated in beams like infrared radiation. It is the absence of heat, and you cannot concentrate it with a parabolic reflector. 
A: Without our atmosphere, the sky would be equivalent to a black body at 3K. A mirror (insulated on the back) would shield you from radiation coming from the ground, effectively making you surrounded by the black body.
With the atmosphere it is more complicated. This paper (see Figure 2) describes using mirror cones to  restrict the angular range of the apparatus to around the zenith direction.
A: Take an object such as a slab of aluminium and expose it to a cloudless night sky. The upper surface will radiate heat to space.
Now position a parabolic reflector under the slab such that the slab is at the focus.
The lower surface of the slab is now exposed to a large area of the night sky to which it will radiate heat.
