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*To*: categories@mta.ca*Subject*: categories: Pullback preserving Set-functors*From*: Tobias Schroeder <tschroed@Mathematik.Uni-Marburg.de>*Date*: Mon, 11 Sep 2000 15:39:51 +0200 (MET DST)*Sender*: cat-dist@mta.ca

I'm interested in proofs of or counterexamples for the following conjectures: Conjecture 1: Any Set-endofunctor that preserves kernels (i.e. pullbacks of a mapping with itself) preserves pullbacks. Conjecture 2: Any Set-endofunctor that preserves kernels *and inverse images* (i.e. pullbacks where one of the mapping is injective) preserves pullbacks. Conjecture 3: Same as Conj. 2 with *and inverse images* replaced by *and equalizers*. Conjecture 4: Same as Conj. 1-3, but concerning *weak* preservation. Conjectur 5: Same as 1-4, but for Set-endofunctors that are subfunctors of a pullback preserving functor. I tried to prove these facts in several ways but was not able to do it or to find a counterexample (the answer to this questions is of some relevance for my work on coalgebras) ... and it looks quite easy, doesn't it? Can somebody help me in this? Thank you very much in advance Tobias Schröder -------------------------------------------------------------- Tobias Schröder FB Mathematik und Informatik Philipps-Universität Marburg WWW: http://www.mathematik.uni-marburg.de/~tschroed email: tschroed@mathematik.uni-marburg.de

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