Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

As in Explicit construction of a initial object in a topos I'm looking an elementary proof of the fact that, in a topos, epimorphisms are stable under pullback or, equivalently, that images are stable under pullback. Stardard proofs uses the fact that the pullback functor has right adjoint, hence it preserve colimit.

Proofs can assume the existence of initial object and the image of a morphisms. In particular I'm looking for a proof wich make uses of the internal logic as here: http://ncatlab.org/nlab/show/Trimble+on+ETCS+III

share|improve this question
Please state the definition of topos you are using, if you are not assuming that pullbacks have right adjoints. –  Zhen Lin Sep 27 '13 at 21:26
I use the elementary definition of topos, namely a cartesian closed category with power objects. –  Fabio Lucchini Sep 27 '13 at 21:28
You can find an "internal logic" proof in [Introduction to higher order categorical logic], Lemma 6.5. –  Zhen Lin Sep 27 '13 at 21:35

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.