Wide field refractor

Hello,
I was wondering if a short refractor, F / 5 or F / 6 achromatic 4 "would be a good telescope for deep sky observation but for the wide-field side, not for details on objects.
But to nebulae and clusters OIII or UHC filters ..? Could compete with this telescope a refractor with ED lens of 80 or 90mm?
regards

Yes, a 4" F/5 or F/6 achromat should do quite well for nebula and clusters. The eye is most sensitive to green light for these faint objects, and a simple achromat should focus green light quite well. For the same reasons it will work well with OIII and UHC filters -- again these are transmitting green light.

Yes, it should compete very well on faint objects with an 80mm or 90mm APO. In fact, what you really need is aperture for faint objects, so the larger 4" will be an advantage.

Of course, the same is NOT true for planets. They are bright enough that the eye can see all the colors, and the achromat's poorer performance at the violet (and to lesser extent red) ends of the spectrum will be obvious.