The colatitude corresponds to the conventional 3D polar angle in spherical coordinates, as opposed to the latitude as used in cartography.
For example, if Alpha Centauri is seen with upper culmination altitude of 72° north (or 108° south) w.r.t.
Stars whose declination absolute value exceed the observer's colatitude in the corresponding hemisphere (see culmination) are called circumpolar because they will never set as seen from that latitude.
If the star's declination absolute value exceed the observer's colatitude in the opposite hemisphere, then it will never be seen from that location.
For example, Alpha Centauri will always be visible at night from Perth, Western Australia (32°S) because the colatitude of Perth is 90° − 32° = 58°, and the declination of Alpha Centauri (-60°) has an absolute value 60 which is greater than 58 in the corresponding hemisphere; on the other hand, the star will never rise in Juneau, Alaska (58°N) because Alpha Centauri's declination absolute value of 60 is more than observer's colatitude (32°) in the opposite hemisphere.