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Cyclic Homology pp 198-222

# The Cyclic Category, Tor and Ext Interpretation

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)

## Abstract

Simplicial objects in an arbitrary category C can be described as functors from the category of non-decreasing maps Δ op to C. Similarly one can construct a category, denoted ΔC and called Connes cyclic category, such that a cyclic object in C can be viewed as a functor from ΔC op to C. The cyclic category ΔC was first described by Connes [1983, where it is denoted Λ or ΔK] who showed how it is constructed out of Δ and the finite cyclic groups.

## Keywords

Simplicial Group Symmetric Group Simplicial Module Braid Group Cyclic Module
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Bibliographical Comments on Chapter 6

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1992

## Authors and Affiliations

1. 1.Institut de Recherche Mathématique AvancéeCentre National de la Recherche ScientifiqueStrasbourgFrance