Yes, the cameras in the iPhone 13 mini and the standard iPhone 13 are the same. In fact, the iPhone 13 mini is essentially the same phone as the iPhone 13 but in a smaller package. You still get 5G support, MagSafe compatibility and, yes, a dual-lens camera system with a 12-megapixel main camera (f/1.6 aperture) and a 12-megapixel ultra wide-angle camera (f/2.4 aperture) and advanced features like Cinematic mode.
The iPhone 13 mini delivers all the power of the standard iPhone 13, with an A15 Bionic processor. Only battery life loses out since the battery is logically smaller, but when we reviewed the phone, we found that it still got us through the day. See our full iPhone 13 review for more details.