TL;DR
This paper reviews recent advances in the categorical framework for D-brane physics, emphasizing homotopy and triangulated categories and their role in homological mirror symmetry from a string theory perspective.
Contribution
It provides an exposition connecting string field theory, homotopy categories, and triangulated categories to D-brane physics and homological mirror symmetry.
Findings
Clarifies the physical basis for categorical structures in D-branes
Highlights the role of homotopy and triangulated categories in string theory
Explores applications to homological mirror symmetry
Abstract
This is an exposition of recent progress in the categorical approach to D-brane physics. I discuss the physical underpinnings of the appearance of homotopy categories and triangulated categories of D-branes from a string field theoretic perspective, and with a focus on applications to homological mirror symmetry.
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