Re: question on finiteness in toposes

Supplementing Peter's answer to Streicher's K-finiteness question, I recall Prop. 7.4 on p. 97 of SLNM #753, which states, for presheaf topoi E = (C^op, Sets), that, with E_Kf the full subcategory of K-finite E-objects: E_Kf is balanced iff it's a topos iff each K-finite is decidable iff C is a "2-way" category iff ... . Streicher's >--> sure isn't 2-way, hence ... . The rest of that 20 year old report on my student Acun~a's thesis with me is also fun. -- Fred