Algebraický seminář
Chiara Sava (MFF UK): Differential graded algebras in differential categories
Abstract: Differential categories provide a categorical framework for the algebraic foundations of differential calculus. Within this setting we can capture familiar notions such as derivations, Kähler differentials, differential algebras and de Rham cohomology. Along this line, in this talk, we will show how to define differential graded algebras in a differential category. In the case of polynomial differentiation, this construction recovers the classical commutative differential graded algebras, while, for smooth functions, it yields differential graded $C^\infty$-rings in the sense of Dmitri Pavlov. To further justify our definition, we will explain how the monad of a differential category can be lifted to its category of chain complexes and how the algebras of the lifted monad correspond precisely to differential graded algebras of the base category, with the free ones given by the de Rham complexes. This is joint work in progress with Jean-Simon Pacaud Lemay.
December 15 - TBA
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.
