Dr. Juan Orendain    


Postdoctoral fellow, part of the project Quantum information Structure of Space Time
QISS project Presentation
Centro de Ciencias Matemáticas CCM,
National University of Mexico UNAM. Campus Morelia.

In the job market 2021-2022

Research interests

Category theory and its applications to the following areas

Online profiles


  • 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/R. Oeckl. Local Functorial Quantum Field Theory: Axiomatic presentation
  • w/R. Oeckl. Local Functorial Quantum Field Theory: Codimension 1 data and involutive functors
  • w/J.A. Zapata. A cubical approach to higher lattice gauge theory.
  • Length one double cateogries via End-indexigs.


List of past courses

Recent talks


Co-organizer of the UNAM categories seminar
Organizer of the Symmetric monoidal framed bicategories seminar


05/24 Group meeting quantum gravity group CCM UNAM
05/30-06/04 MSRI workshop on Higher Categories and Categorification 
06/12-06/17 BIRS CMO workshop on Mathematical and Conceptual Aspects of Quantum Theory

Past activities

List of past activities

Books, papers, etc.



Resources in applied category theory

Spanish version