One-sided exact categories

Quantum One-Sided Exact Error Algorithms

We define a complexity class for randomized algorithms with one-sided error that is exactly equal to a constant (unlike the usual definitions, in which the error is only bounded above or below by a constant). We show that the corresponding quantum classes (one each for a different error probability) are in fact all equivalent to each other and to EQP, the quantum analogue of P. The technique us...

One-Sided Interval Trees

We give an alternative treatment and extension of some results of Itoh and Mahmoud on one-sided interval trees. The proofs are based on renewal theory, including a case with mixed multiplicative and additive renewals.

Exact Categories Theo Bühler

We survey the basics of homological algebra in exact categories in the sense of Quillen. All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3×3-lemma and the snake lemma. We briefly discuss exact functors, idempotent completion and weak idempotent completeness. We then show that it is possible to construct the derived category of an exact category without any em...

Exact Categories and Duality

Throughout the book Homological algebra, by H. Cartan and S. Eilenberg, the authors dealt with functors defined on categories of modules over certain rings and whose values again were modules over a ring. It will be shown in this paper that the theory may be generalized to functors defined on abstract categories, and whose values are again in such abstract categories. An abstract treatment such...

One - sided Versus Two - sided Error in