Goodwillie's calculus via relative homological algebra. The abelian case
Teimuraz Pirashvili
TL;DR
This paper explains how elementary relative homological algebra concepts can be used to construct the Taylor tower for functors from pointed categories to abelian groups, aligning with Johnson and McCarthy's work.
Contribution
It demonstrates a new approach to building the Taylor tower using basic relative homological algebra, simplifying and clarifying previous constructions.
Findings
Constructs the Taylor tower via elementary relative homological algebra.
Recovers Johnson and McCarthy's constructions in the abelian case.
Provides a clearer conceptual framework for functor calculus.
Abstract
We will explain how elementary concepts of relative homological algebra yield the Taylor tower for functors from pointed categories to abelian groups recovering the constructions of Johnson and McCarthy.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Logic, programming, and type systems