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.

jorendain[at]matmor.unam.mx

In the job market 2021-2022

Research interests

Category theory and its applications to the following areas

Online profiles

Publications/preprints

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.

Teaching

List of past courses

Recent talks

2021: Globularly generated double categories: Then and now. CaTCat: Open House on Category Theory 2021. Mexico City, Mexico. Slides.
2021: Por qué y cómo categorificar una teoría cuántica de campos. Coloquio PCCM. CCM UNAM. Morelia Mexico. Slides.
2021: Length of framed bicategories. Category Theroy 2021. CT20->21. Genoa. Italy.
2021: Length 1 double categories via End-indexings. Special session on cateogries and topology, MCA2021 Buenos Aires. Argentina. Slides.
2021: Open Petri nets and symmetric monoidal double categories. [In Spanish] Petri nets reading seminar. Slides.
2021: How long does it take to frame a bicategory. New York City category theory seminar. Video. Slides.
2021: The rate equation and the master equation for stochastic Petri nets [In Spanish] Petri nets reading seminar. Slides.
2021: Operational semantics for Petri nets as commutative monoidal categories [In Spanish]. Petri Nets reading seminar. Slides.
2021: Remarks on the bicategory of von Neumann algebras. QSSS, Ohio State University. US. Slides
2020: Remarks on the bicategory of von Neumann algebras. UFSC C*-algebras seminar. UFSC. Brazil. Slides. Video.
2020: Categorías dobles de álgebras de von Neumann. Segundo cíclo de conferencias. [In Spanish] Facultad de Ciencias UNAM. Slides. Video.
2020: Globularly generated double categories. MIT categories seminar. MIT. US. Slides. Video.
2020: Double categories of factors. Noncommutative Geometry Seminar at the University of Copenhagen. Denmark. Slides.
2020: Formal Haagerup standard form on infinite index morphisms of factors. Groups, Operators, and Banach Algebras Webinar. Lancaster University. UK. Slides.
2020: Internal categories of factors. Zagreb Workshop on Operator Theory. University of Zagreb. Zagreb, Croatia. Slides. Video.
2020: Formal Haagerup standard form on infinite index morphisms of factors. Canadian Operator Symposium, Fields Institute, Canada. Slides
2020: Globularly generated double categories. Extending functors and filling squares. [In Spanish] UAM-I. Slides

Organization

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

Activities

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.

Bookshelf

Resources

Resources in applied category theory

Spanish version