Why Higher Category Theory in Physics? - Comments

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Discussion Overview

The discussion centers around the relevance and application of higher category theory in physics, particularly in relation to concepts such as branes and higher gauge theory. Participants explore the mathematical foundations and potential physical implications, as well as the challenges of connecting abstract mathematics to tangible physical problems.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants express that n-categories can explain the equivalence of different integration orders in higher gauge theory, suggesting a connection to physical concepts like branes.
  • One participant emphasizes the importance of group structures in lattice gauge theory, noting that 2-groups are necessary for consistent labeling of edges and plaquettes.
  • Another participant argues that without a connection to physical problems beyond gravity, higher category theory may be perceived as lacking practical utility.
  • Some participants advocate for the intrinsic value of mathematics, suggesting that even if immediate applications are not evident, learning higher category theory could yield benefits in the future.
  • Concerns are raised about the need for compelling arguments to persuade physicists of the relevance of higher category theory, with calls for practical applications or simplifications in calculations.
  • A later reply acknowledges misunderstandings and suggests that a broader exposition on the topic could help clarify its significance in physics.

Areas of Agreement / Disagreement

Participants express a mix of skepticism and curiosity regarding the applicability of higher category theory in physics. While some see potential value, others question its relevance without clear connections to experimental realities. There is no consensus on the utility or importance of higher category theory in the context of physical problems.

Contextual Notes

Some participants note the limitations in understanding and the need for clearer connections between abstract mathematical concepts and physical applications. There is also mention of the historical context of mathematical approaches in physics, which may influence current perceptions.

  • #31
[URL='https://www.physicsforums.com/insights/author/urs-schreiber/']Urs Schreiber[/URL] said:
Remarkably, homotopy theory is a "smaller theory": it arises from classical theory by removing axioms from classical logic. This is the fantastic insight of homotopy type theory.

Well, larger versus smaller or simpler versus more complex depends on how you measure things. You can understand classical mathematics as being a simplification of constructive mathematics, in which you toss out distinctions. (such as the distinction between a proof of ##A## and a proof of ##\neg \neg A##)
 

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