This note covers the following
topics: Conventions, Differential graded algebras, Differential graded
modules, The homotopy category, Cones, Admissible short exact sequences,
Distinguished triangles, Cones and distinguished triangles, The homotopy
category is triangulated, Projective modules over algebras, Injective modules
over algebras, P-resolutions, I-resolutions, The derived category, The canonical
delta-functor, Linear categories, Graded categories, Differential graded
categories, Obtaining triangulated categories, Tensor product, 24. Derived
tensor product, Variant of derived tensor product, Characterizing compact
objects and Equivalences of derived categories.
This PDF book
covers the following topics related to Differential Algebra : Basic Differential Algebra, Derivations and Dual Numbers, Differential
Ideals and Ritt Noetherianity, Characteristic Sets and the Partial
Ritt-Raudenbush, Basic Differential Algebraic Geometry: Properties of the
Kolchin Topology, Differentially Closed Fields, Differential Dimension
Polynomials, Differential Galois Theory, Binding Groups and Internality,
Pillay’s X-strongly-normal theory, Galois Theory of Linear Differential
Equations, Algebraic D-Groups and Logarithmic Derivatives, Constrained
Cohomology, The Galois Groupoid, Differential Algebraic Groups,
Preliminaries from Model Theory.
This PDF book covers the following topics related to Differential
Algebra : Foundations of Differential Algebra, the Ring of
Differential Polynomials and Its Ideals, Differential Algebraic Extensions,
Differential Galois Theory, Linear Algebraic Groups, Liouvillian
Extensions.
Author(s): Alexey Ovchinnikov, Maxwell Shapiro, Peter
Thompson
This note covers the following
topics: Conventions, Differential graded algebras, Differential graded
modules, The homotopy category, Cones, Admissible short exact sequences,
Distinguished triangles, Cones and distinguished triangles, The homotopy
category is triangulated, Projective modules over algebras, Injective modules
over algebras, P-resolutions, I-resolutions, The derived category, The canonical
delta-functor, Linear categories, Graded categories, Differential graded
categories, Obtaining triangulated categories, Tensor product, 24. Derived
tensor product, Variant of derived tensor product, Characterizing compact
objects and Equivalences of derived categories.
This note introduces
both, state some of their basic properties, and explain connections to o-minimal
structures. Also describe a common algebraic framework for these examples: the
category of H-fields. This unified setting leads to a better understanding of
Hardy fields and transseries from an algebraic and model-theoretic perspective.