# TRIPLES, ALGEBRAS AND COHOMOLOGY

@inproceedings{Beck1967TRIPLESAA, title={TRIPLES, ALGEBRAS AND COHOMOLOGY}, author={Jonathan Beck}, year={1967} }

It is with great pleasure that the editors of Theory and Applications of Categories make this dissertation generally available. Although the date on the thesis is 1967, there was a nearly complete draft circulated in 1964. This thesis was a revelation to those of us who were interested in homological algebra at the time. Although the world’s very first triple (now more often called “monad”) in the sense of this thesis was non-additive and used to construct flabby resolutions of sheaves…

## 174 Citations

### Composite cotriples and derived functors

- Mathematics
- 1969

The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)].…

### Algebraic deformations and triple cohomology

- Mathematics
- 1980

The fundamental theorems of algebraic deformation theory are shown to hold in the context of enriched triple cohomology. This unifies and generalizes the classical theory. The fundamental results in…

### Two cohomology theories for structured spaces

- Mathematics
- 2020

In [1] we defined a new kind of space called 'structured space' which locally resembles, near each of its points, some algebraic structure. We noted in the conclusion of the cited paper that the maps…

### Symmetric homology over rings containing the rationals

- Mathematics
- 1973

Let R be a commutative ring with unit which contains the rational numbers. Let A be a commutative R-algebra. In this paper we prove that the cotriple homology and cohomology modules of R for the…

### Relative Barr-Rinehart and cotriple cohomology groups are isomorphic

- Mathematics
- 1984

The theorem, stated in the title of this article, is proved. Several people have asked about the relationship between the relative cohomology groups defined by Barr and Rinehart [3], and those of…

### RELATIVE BARR-RINEHART AND COTRIPLE COHOMOLOGY GROUPS

- Mathematics
- 2010

The theorem, stated in the title of this article, is proved. Several people have asked about the relationship between the relative cohomology groups defined by Barr and Rinehart [3], and those of…

### Homological Algebra for Superalgebras of Differentiable Functions

- Mathematics
- 2012

This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we…

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