Proseminarvortrag in Aachen, WS 04/05
Skript Lineare Algebra für Informatikerdvipspdf (Version 12.02.10)
Vorlesung in Ulm, WS 02/03 und WS 03/04. A counterexample on nilpotent endomorphisms in triangulated categories dvipspdf
We give a counterexample to an assertion on nilpotent endomorphisms of degree 3 in triangulated categories. Roughly speaking, it is in general not possible to lower the nilpotency degree by
passing to a certain cone.
(jt. w. Theo Bühler) Some elementary considerations in exact categories dvipspdf (Version 23.06.10)
We give counterexamples to some elementary assertions in exact categories and derive some lemmata directly from the axioms.
Dweak squares in Heller triangulated categoriesdvipspdf
We discuss a compatibility between distinguished weak (dweak) squares with the shift functor, which holds in a closed Heller triangulated category. It can be formulated in a Verdier triangulated
category as well, but I do not know whether it can be proven there.
Remarks on the axioms for exact categories: (Ex 2) is redundant; if idempotents split, then first to pure mono is pure mono dvipspdf
The axiom (Ex 2) in the axiomatisation of exact categories as in "Heller triangulated categories"
§A.2, is redundant. Moreover, if idempotents split, then the first morphism in a composition yielding a pure monomorphism, is purely monomorphic.
A construction principle for Frobenius categories dvipspdf
This is a supplement to "Heller triangulated categories"
We exhibit a structure of a Frobenius category on a category of diagrams appearing in loc. cit., using a general principle.
A relative Yoneda Lemmadvipspdf
We construct set-valued right Kan extensions via a relative Yoneda Lemma.
On the center of the derived category dvipspdf
Rickard observed that in general, the center of the bounded derived category of a ring is strictly bigger than the center of the ring (unpublished). We give a simple example.
Does "Quillen A with an extra direction" hold?dvipspdf
The assertion in question is a bicategorical version of Quillen A, where in the "new" direction "nothing happens". I do not know whether it holds or not.
I also sketched an idea how one might approach this question. I would be grateful for arguments, counterexamples (also to that idea), references, for anything.