Ads
related to: methods of homological algebra worksheet free printable 7teacherspayteachers.com has been visited by 100K+ users in the past month
- Assessment
Creative ways to see what students
know & help them with new concepts.
- Worksheets
All the printables you need for
math, ELA, science, and much more.
- Assessment
Search results
Results from the WOW.Com Content Network
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology ) and abstract algebra (theory of modules and syzygies ) at the end of the 19th century, chiefly by ...
In the simplest possible case the relationship is that of a tensor product, but for applications it is very often necessary to apply certain tools of homological algebra to express the answer. A Künneth theorem or Künneth formula is true in many different homology and cohomology theories, and the name has become generic.
In other cases, such as for group homology, there are multiple common methods to compute the same homology groups. In the language of category theory , a homology theory is a type of functor from the category of the mathematical object being studied to the category of abelian groups and group homomorphisms, or more generally to the category ...
Much of homological algebra is clarified and extended by the language of triangulated categories, an important example being the theory of sheaf cohomology. In the 1960s, a typical use of triangulated categories was to extend properties of sheaves on a space X to complexes of sheaves, viewed as objects of the derived category of sheaves on X ...
In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957 [1] in order to develop the machinery of homological algebra for modules and for sheaves in a unified manner. The theory of these categories was further developed in Pierre Gabriel's 1962 thesis.
The usual proof of this result is a pure piece of homological algebra about chain complexes of free abelian groups. The form of the result is that other coefficients A may be used, at the cost of using a Tor functor .
Ads
related to: methods of homological algebra worksheet free printable 7teacherspayteachers.com has been visited by 100K+ users in the past month