Fibered Multiderivators and (co)homological descent
نویسنده
چکیده
The theory of derivators enhances and simplifies the theory of triangulated categories. In this article a notion of fibered (multi-)derivator is developed, which similarly enhances fibrations of (monoidal) triangulated categories. We present a theory of cohomological as well as homological descent in this language. The main motivation is a descent theory for Grothendieck’s six operations.
منابع مشابه
Homotopy Limits and Colimits in Nature A Motivation for Derivators
An introduction to the notions of homotopy limit and colimit is given. It is explained how they can be used to neatly describe the “old” distinguished triangles and shift functors of derived categories resp. cofiber and fiber sequences in algebraic topology. One of the goals is to motivate the language of derivators from the perspective of classical homological algebra. Another one is to give e...
متن کاملAbelian Quotients of Monoids of Homology Cylinders
We discuss abelian quotients of monoids of homology cylinders of a surface, each of which consists of a compact 3-manifold as a homology cobordism between two copies of a surface and markings of the boundary. We show that both of the monoid of all homology cylinders and that of irreducible homology cylinders are not finitely generated and moreover they have big abelian quotients. The proof is g...
متن کاملHeegaard Gradient of Seifert 3-manifold
The infimal Heegaard gradient of a compact 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3-manifolds, and show that a Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it it virtually fibers over the circle or over a surface other than the 2-sphe...
متن کاملOn descent for coalgebras and type transformations
We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...
متن کاملTeichmüller Polynomials, Alexander Polynomials and Finite Covers of Surfaces
In this article we explore a connection between finite covers of surfaces and the Teichmüller polynomial of a fibered face of a hyperbolic 3–manifold. We consider the action of a homological pseudo-Anosov homeomorphism ψ on the homology groups of a class of finite abelian covers of a surface Σg,n. Eigenspaces of the deck group actions on these covers are naturally parametrized by rational point...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015