This e-book encompasses a sequence of lectures that explores 3 assorted fields during which functor homology (short for homological algebra in functor different types) has lately performed an important function. for every of those purposes, the functor standpoint offers either crucial insights and new tools for tackling tricky mathematical problems.

In the lectures through Aurélien Djament, polynomial functors seem as coefficients within the homology of countless households of classical teams, e.g. normal linear teams or symplectic teams, and their stabilization. Djament’s theorem states that this solid homology should be computed utilizing merely the homology with trivial coefficients and the potential functor homology. The sequence comprises an interesting improvement of Scorichenko’s unpublished results.

The lectures by way of Wilberd van der Kallen result in the answer of the final cohomological finite new release challenge, extending Hilbert’s fourteenth challenge and its approach to the context of cohomology. the focal point here's at the cohomology of algebraic teams, or rational cohomology, and the coefficients are Friedlander and Suslin’s strict polynomial functors, a conceptual kind of modules over the Schur algebra.

Roman Mikhailov’s lectures spotlight topological invariants: homoto

py and homology of topological areas, via derived functors of polynomial functors. during this regard the functor framework makes larger use of naturality, permitting it to arrive calculations that stay past the seize of classical algebraic topology.

Lastly, Antoine Touzé’s introductory path on homological algebra makes the publication available to graduate scholars new to the field.

The hyperlinks among functor homology and the 3 fields pointed out above supply compelling arguments for pushing the improvement of the functor perspective. The lectures during this e-book will supply readers with a suppose for functors, and a useful new standpoint to use to their favorite problems.