Speaker:
Rosanna Laking

Title: Definability and approximation theory in triangulated categories

Title: Definability and approximation theory in triangulated categories

Abstract:
Approximation theory allows one to study the category of
R-modules Mod(R) via subcategories whose objects “approximate”
arbitrary modules in Mod(R) i.e. precovering and preenveloping
subcategories. This fruitful theory has made many
important contributions towards classification problems in
Representation Theory.

In
this talk I will report on joint work with Jorge Vitòria, in
which we develop a parallel techniques for algebraic compactly
generated triangulated categories (e.g. derived module
categories). In this setting there are some obstructions
to the development of the theory of approximations. The
main problem is that precovers and preenvelopes in module
categories are typically constructed using limits or colimits,
which rarely exist in triangulated categories. Our
approach is to make use of the abelian and exact categories
underlying the construction of algebraic compactly generated
triangulated categories to transfer the classical results to the
triangulated setting. In particular, our techniques allow
us to show that definable subcategories have good approximation
properties.