Representable triangulated functors in terms of semiorthogonal decompositions

TL;DR

This paper extends Bondal and Kapranov's theorem to triangulated functors, providing a new perspective on representing cohomological functors through semiorthogonal decompositions in enriched category theory.

Contribution

It generalizes the existing theorem to triangulated functors and introduces relevant terminology in enriched category theory.

Findings

Provides a version of the theorem for triangulated functors

Introduces terminology in enriched category theory

Transfers the original proof to the new setting

Abstract

A theorem of Bondal and Kapranov lifts representations of cohomological functors from semiorthogonal decompositions of triangulated categories. We present a version of this result for triangulated functors. To this end, we introduce suitable terminology in enriched category theory and transfer the original proof.