Obstructions in a model category and Klein and Williams' intersection invariants

TL;DR

This paper introduces a new obstruction invariant in model categories, inspired by Klein and Williams' intersection theory, which unifies lift and extension obstructions under certain dimension and connectivity conditions.

Contribution

It develops a novel, unified obstruction invariant in model categories, extending classical intersection theory concepts to a broader categorical framework.

Findings

The invariant effectively detects lift and extension obstructions.

It generalizes classical algebraic topology obstructions.

The invariant is complete under suitable dimension and connectivity assumptions.

Abstract

We give an obstruction for lifts and extensions in a model category inspired by Klein and Williams' work on intersection theory. In contrast to the familiar obstructions from algebraic topology, this approach produces a single invariant that is complete in the presences of the appropriate generalizations of dimension and connectivity assumptions.