Would the reflection of a 4-dimensional "object" be 3-dimensional?

According to this wiki article, if you were to shine light on a 4th dimensional object in a 4th dimensional universe, the shadow of this 4th dimensional object would be 3-dimensional.If a light is shone on a three-dimensional object, a two-dimensional shadow is cast. By dimensional analogy, light shone on a two-dimensional object in a two-dimensional world would cast a one-dimensional shadow, and light on a one-dimensional object in a one-dimensional world would cast a zero-dimensional shadow, that is, a point of non-light. Going the other way, one may infer that light shone on a four-dimensional object in a four-dimensional world would cast a three-dimensional shadow. https://ift.tt/3ly1Fht reflection of a 3-dimensional object in a mirror is 2-dimensional. Would the reflection of a 4-dimensional object in some kind of 4th-dimensional mirror be 3-dimensional?Thank you!