This is the Şeyh Ibrahim Tennüri Türbesi (grave monument) from 1482.

Its pyramidal roof in late-Seljuk style is almost anachronistic, Kayseri being under definitive Ottoman rule since almost fifty years at the time. Inside the tomb, three cenotaph sarcophagi, belonging to Şeyh İbrahim Tennûrî, his son and a grandson, who were Şeyhs also (‘Sheikh’ has a lot of meanings; in this particular case, the man, always an elder, is the spiritual leader of his congregation).

İbrahim Tennuri was a Sufi, from the Bayramiye Order (founded by Hacı Bayram from Ankara). He became close to Akşemseddin, the teacher and Şeyh ul-Islâm of sultan Mehmed II, and so became a confidant of the sultan himself. Akşemseddin sent Şeyh Ibrahim to Kayseri as his and sultan Mehmed’s representative, where he founded a tekke (dervish house) and became quite famous as an islamic scholar, philosopher and poet.

Correspondent: J.M.Criel, Antwerpen.
Sources: ‘Tarihi Kayseri Cami ve Mescidleri’ – Doç. Ilhan Özkeçeci (1997) & Wikipedia .