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ON DETERMINANT FUNCTORS AND KTHEORY
, 1006
"... Abstract. In thispaper weintroduce a newapproach to determinantfunctors which allows us to extend Deligne’s determinant functors for exact categories to Waldhausen categories, (strongly) triangulated categories, and derivators. We construct universal determinant functors in all cases by original met ..."
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Abstract. In thispaper weintroduce a newapproach to determinantfunctors which allows us to extend Deligne’s determinant functors for exact categories to Waldhausen categories, (strongly) triangulated categories, and derivators. We construct universal determinant functors in all cases by original methods which are interesting even for the known cases. Moreover, we show that the target of each universal determinant functor computes the corresponding Ktheory in dimensions 0 and 1. As applications, we answer open questions by Maltsiniotis and Neeman on the Ktheory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity and localization theorems for lowdimensional Ktheory and
SMASH PRODUCTS FOR SECONDARY HOMOTOPY GROUPS
, 2006
"... Abstract. We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cupone products, Toda brackets and Whitehead products are considered. Contents ..."
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Abstract. We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cupone products, Toda brackets and Whitehead products are considered. Contents
unknown title
, 2006
"... Abstract. We give a small functorial algebraic model for the 2stage Postnikov section of the Ktheory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors. ..."
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Abstract. We give a small functorial algebraic model for the 2stage Postnikov section of the Ktheory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.
unknown title
, 2006
"... Abstract. We give a small functorial algebraic model for the 2stage Postnikov section of the Ktheory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors. ..."
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Abstract. We give a small functorial algebraic model for the 2stage Postnikov section of the Ktheory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.
THE SYMMETRIC ACTION ON SECONDARY HOMOTOPY GROUPS
, 2006
"... Abstract. We show that the symmetric track group Sym □ (n), which is an extension of the symmetric group Sym(n) associated to the second StiefelWithney class, acts as a crossed module on the secondary homotopy group of a pointed space. ..."
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Abstract. We show that the symmetric track group Sym □ (n), which is an extension of the symmetric group Sym(n) associated to the second StiefelWithney class, acts as a crossed module on the secondary homotopy group of a pointed space.