Differential homological algebra and homogeneous spaces

Abstract harmonic analysis, homological algebra, and operator spaces

harmonic analysis, homological algebra, and operator spaces

Homological Algebra

Categories and Homological Algebra

The aim of these Notes is to introduce the reader to the language of categories with emphazis on homological algebra. We treat with some details basic homological algebra, that is, categories of complexes in additive and abelian categories and construct with some care the derived functors. We also introduce the reader to the more sophisticated concepts of triangulated and derived categories. Ou...

Homological Algebra and Data

These lectures are a quick primer on the basics of applied algebraic topology with emphasis on applications to data. In particular, the perspectives of (elementary) homological algebra, in the form of complexes and co/homological invariants are sketched. Beginning with simplicial and cell complexes as a means of enriching graphs to higher-order structures, we define simple algebraic topological...

Homology and Homological Algebra,

= convex hull of {a0, . . . , an}. The points a0, . . . , an are geometrically independent if a1 − a0, . . . , an − a0 is a linearly independent set over R. Note that this is independent of the order of a0, . . . , an. In this case, we say that the simplex a0 . . . an is n -dimensional, or an n -simplex. Given a point Pn i=1 λiai belonging to an n-simplex, we say it has barycentric coordinates ...