How to explain the equation 'Altitude of a star at culmination = co-latitude + declination'?
Unless the observer is at a geographic pole, the celestial equator is not parallel to the horizon but crosses it at an angle equal to the observer's colatitude.
A star's path across the sky is parallel to the celestial equator, with maximum altitude midway between the eastern and western horizons, i.e. on the meridian.

Rendered by Stellarium