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Coherence for adjunctions in a $3$-category via string diagrams

Manuel Araújo

Abstract

We define a coherent adjunction in a strict $3$-category and we use string diagrams to show that any adjunction can be extended to a coherent adjunction in an essentially unique way.

Coherence for adjunctions in a $3$-category via string diagrams

Abstract

We define a coherent adjunction in a strict -category and we use string diagrams to show that any adjunction can be extended to a coherent adjunction in an essentially unique way.

Paper Structure

This paper contains 24 sections, 42 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. Pullbacks and the long exact sequence for a fibration
  3. Relation to other work
  4. Future work
  5. Definitions and basic results
  6. Strict $n$-categories
  7. Equivalences
  8. Adjunctions
  9. Presentations
  10. String diagrams
  11. Functor categories
  12. Natural transformations
  13. Modifications
  14. Perturbations
  15. Fibrations
  16. ...and 9 more sections

Key Result

Theorem 1.1

Given a strict $3$-category $\mathcal{C}$, the restriction map is a weak equivalence of strict $3$-groupoids.

Theorems & Definitions (108)

  • Theorem 1.1: Main Theorem
  • Remark 1.2
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition 2.8
  • ...and 98 more