Cotilting Torsion Classes and Envelope Comodules

To study the relationship between cotilting torsion classes and envelope comodules over a coalgebra, the definitions of (pre)envelopes and finendo for comodules were first introduced and their properties were studied. Then, the maximal cotilting comodules and envelope comodules were introduced, improving that there exists a bijection between the cotilting torsion classes and the maximal cotilting comodules. Finally, it is represented by envelope comodules over a coalgebra when the cotilting torsion class is an envelope class.