On The Cohomology of Categories

Year 1973, Volume: 22 , 0 - 0, 01.01.1973

Georges Hoff

https://doi.org/10.1501/Commua1_0000000638

Abstract

We have started our study of the cohomology of categories [1] in particularizing a note of C. Ehresmann [2]. Then, our wislı was to put together, in a same work, our original study and the theory of M. Andre [3 ]. The result is the text herewith presen- ted.
In the first chapter, we construct a homology and a coho- mology of categories. The cohomology is a generalization (dif- ferent of the one defined in [2]) of the cohomology considered in [1]. The homology is the very same as the one defined in [3].
In the second chapter, we particularize the previous theory in order to obtain a cohomology of the smaU categories which generalizes the classical cohomology of the groups, a group heing a particular category.
These two chapters are written in a different mind; conse- quently, we have judged useful to differentiate their notations.
We could use also the tools herewith introduced, for example, in a generalization of the study of the groups operating on topo- logical spaces; this wiU be the subject of an other publication.

Keywords

Cohomology, Categories, Statistics

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi