Classifying vectoids and operad kinds (Q641941)

This paper presents an original, beautiful and brave generalization of the construction of the universal topos, called vectoid. It is used to construct classifying vectoids associated to an algebra or a coalgebra. Such classifying vectoids give examples of vectoids not coming from spaces known before (such as ringed topoi). Moreover, monoids in the endomorphism categories of these classifying vectoids turn out to provide a systematic approach to constructing a different versions of the notion of operads, as well as generalizations not known before.