Juan Orendain, PhD      

VAP at the MAMS department at Case Western Reserve University
E-mail juan.orendain [at] case [dot] edu

Research interests

Higher category theory and its applications to:

  • Topology
  • Quantum field theory
  • Operator algebras
  • Representation theory

Online profiles


  • w/R. Oeckl. Compositional Quantum Field Theory: An axiomatic presentation. Pereprint vers.
  • Free globularly generated double categories II: The canonical double projection. Cahiers de topologie et géometrie différentielle catégoriques Vol. LXII (2021) Issue 3. pp 243-302 Preprint vers. Journal vers. 
  • Free globularly generated double categories I. Theory and Applications of Categories Vol. 34 No.42, pp 1343-138. Preprint vers. Journal vers.
  • Lifting bicategories into double categories: The globularly generated condition. Theory and Applications of Categories, Vol. 34, No. 4, pp 80-108. Preprint vers.  Journal vers.
  • Combinatorial dimensions: Indecomposability of certain local trivial extension algebras. Journal of Algebra an Applications, 13, No. 06. Preprint vers. Journal vers.
  • On direct sum decompositions of Krull-Schmidt artinian modules. Journal of Algebra and Applications, 13, No. 03. Preprint vers. Journal vers.
  • Lifting bicategories through the Grothendieck construction. Submitted. Preprint vers.
  • Cylinder topological quantum field theory: A categorical presentation of classical field theory and its symmetries. Preprint vers.
  • A note on the existence of essential indecomposable submodules of Ore domains. Preprint vers.

In preparation

  • w/Nick Gurski and David Yetter. Compact closed bicategories.
  • w/R. Oeckl. Compositional Quantum Field Theory II: State spaces and involutive symmetric monoidal functors
  • w/J.A. Zapata. A cubical approach to higher lattice gauge theory.
  • w/Rubén Maldonado. Length 1 internalizations via End-indexing.


Fall 2023

Math 308 Abstract Algebra
Math 401 Graduate Abstract Algebra I

Spring 2023

Math 402 Abstract Algebra II
Math 462 Algebraic Topology
Math 601 Reading seminar on Markov categories, with Mark Meckes

List of past courses

Recent talks



Spring 2023

co-organizer of Math 601, reading seminar on categorical probability, with Mark Meckes.

Previous events and seminars organized


  • Rubén Maldonado, PhD, CCM, UNAM
  • Iván Sánchez Silva, PhD, co-mentoring with José Antonio Zapata, CCM, UNAM
  • Brian Zhang, Capston project. Case Western Reserve University.
  • Sam Reeder, Capston project. Case Western Reserve University.


Past activities

List of past activities

Books, papers, etc.



Resources in applied category theory