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Decompositions of the category of noncommutative sets and Hochschild and cyclic homology

Jolanta Słomińska (2003)

Open Mathematics

In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.

Differentials in the homological homotopy fixed point spectral sequence.

Bruner, Robert R., Rognes, John (2005)

Algebraic & Geometric Topology

Dilogarithm, grassmannian complex and scissors congruence groups of algebraic polyhedra

Masaki Hanamura (1995)

Compositio Mathematica

Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere.

Ausoni, Christian, Dundas, Bjørn Ian, Rognes, John (2008)

Documenta Mathematica

Dualization in algebraic K-theory and the invariant e¹ of quadratic forms over schemes

Marek Szyjewski (2011)

Fundamenta Mathematicae

In the classical Witt theory over a field F, the study of quadratic forms begins with two simple invariants: the dimension of a form modulo 2, called the dimension index and denoted e⁰: W(F) → ℤ/2, and the discriminant e¹ with values in k₁(F) = F*/F*², which behaves well on the fundamental ideal I(F)= ker(e⁰). Here a more sophisticated situation is considered, of quadratic forms over a scheme and, more generally, over an exact category with duality. Our purposes are: ...