https://www.math.ucla.edu/~dpenneys/MoritaEquivalence.pdf
Categorified Morita equivalence These notes were compiled from the following sources: • Rieffel’s “Morita Equivalence for C∗ -algebras and W∗ -algebras” • Mueger’s “From subfactors to categories and topology I” (arXiv:math/0111204) • Ostrik’s “Module categories, weak Hopf algebras and modular invariants” (arXiv:math/0111139) • Etingof, Nikshych, and Ostrik’s “Fusion categories and homotopy theory”
Temperley Lieb Diagrams and 2-Categories David Penneys 4/14/08 (1) Simplicial Resolutions. Let F : C → D be a left adjoint to U : D → C, and denote by σ (respectively δ) the unit (respectively counit) of the adjunction. So σ(d) ∈ D(d, UF(d)) cor
Temperley Lieb Diagrams and 2-Categories David Penneys 4/14/08 (1) Simplicial Resolutions. Let F : C → D be a left adjoint to U : D → C, and denote by σ (respectively δ) the unit (respectively counit) of the adjunction. So σ(d) ∈ D(d, UF(d)) corresponds to idF(d) and δ(c) ∈ C(FU(c), c) to idU(c). (a) For any object c ∈ C, show that the following formulas define a simplicial object ⊥• (c) in C: Let
https://www.math.ucla.edu/~dpenneys/PenneysUCBThesis2012.pdf
Planar structure for inclusions of finite von Neumann algebras by David Signorielli Penneys A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Vaughan F. R. Jones, Chair Professor Marc A. Rieffel Professor Ori Ganor Spring 2012 Pla
http://www.math.ucla.edu/~dpenneys/MoritaEquivalence.pdf
Categorified Morita equivalence These notes were compiled from the following sources: • Rieffel’s “Morita Equivalence for C∗ -algebras and W∗ -algebras” • Mueger’s “From subfactors to categories and topology I” (arXiv:math/0111204) • Ostrik’s “Module categories, weak Hopf algebras and modular invariants” (arXiv:math/0111139) • Etingof, Nikshych, and Ostrik’s “Fusion categories and homotopy theory”
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