منابع مشابه
Third Mac Lane Cohomology via Categorical Rings
In the fifties, Saunders Mac Lane invented a cohomology theory of rings using the cubical construction introduced earlier by Eilenberg and himself to calculate stable homology of Eilenberg-Mac Lane spaces. As shown in [9], this theory coincides with the topological Hochschild cohomology for Eilenberg-Mac Lane ring spectra. In particular, the third dimensional cohomology group is expected to pro...
متن کاملThe strength of Mac Lane set theory
SAUNDERS MAC LANE has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system ZBQC of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, TCo, of Transitive Containment, we shall refer as MAC. His system is naturally ...
متن کاملHomological Localizations of Eilenberg-mac Lane Spectra
We discuss the Bousfield localization LEX for any spectrum E and any HR-module X, where R is a ring with unit. Due to the splitting property of HR-modules, it is enough to study the localization of Eilenberg– MacLane spectra. Using general results about stable f -localizations, we give a method to compute the localization of an Eilenberg–MacLane spectrum LEHG for any spectrum E and any abelian ...
متن کاملDuality and Eilenberg - Mac Lane Spectra
Stable cohomotopy groups of Eilenberg-Mac Lane spectra of finite groups are shown to be trivial. This implies that the stable homotopy category, which is large enough to represent ordinary cohomology theory, cannot be self-dual. It can also be interpreted as an evidence to support Freyd's generating hypothesis and a proof of a stable version of a conjecture of D. Sullivan.
متن کاملThe theory of opetopes via Kelly-Mac Lane graphs
This paper follows from the work of [4] and [3]. In the former paper we give an explicit construction of opetopes, the underlying cell shapes in the theory of opetopic n-categories; at the heart of this construction is the use of certain trees. In the latter paper we give a description of trees using Kelly-Mac Lane graphs. In the present paper we apply the latter to the former, to give a constr...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2008
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s030500410700076x