Dr. Juan Orendain

Visiting Assistant Professor at Case Western Reserve University
E-mail juan.orendain[ at] case [dot] edu

Research interests

Category theory and its applications to the following areas

Online profiles

Publications/preprints

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/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.
Length one double cateogries via End-indexigs.

Recent talks

2022

Reconstructing double categories from End-indexings. Conference on Functor Categories, Model Theory, and Constructive Category Theory. University of Almería, Almería. Spain
Equivariant Functorial Quantum Field Theory. BIRS CMO Workshop on Mathematical and Conceptual Apects of Quantum Theory
Higher lattice gauge fields and cubical omega-groupods. Higher Structures Seminar, Feza Gürsey Center for Physics and Mathematics.
Globularly generated double categories. Mathematics Colloquium Yeditepe University, Istambul, Turkey.
Composicionalidad categórica: De modelos de epidemiología y diseño de software a gravedad cuántica. coloquio departamento de Matemáticas ITAM
Quantum field theory in the GBF from TQFT. Quantum Foundations group meeting CCM UNAM
Topological quantum field theory as symmetric monoidal functors quantum foundations group meeting CCM UNAM
Categories, fields and information theory. quntum foundations group meeting CCM UNAM
Operational semantics on Petri nets. Escuela Oaxaqueña de matemáticas. IMATE UNAM Unidad Oaxaca.

2021

2020

Remarks on the bicategory of von Neumann algebras. UFSC C*-algebras seminar. UFSC. Brazil. Slides. Video.
Categorías dobles de álgebras de von Neumann. Segundo cíclo de conferencias. [In Spanish] Facultad de Ciencias UNAM. Slides. Video.
Globularly generated double categories. MIT categories seminar. MIT. US. Slides. Video.
Double categories of factors. Noncommutative Geometry Seminar at the University of Copenhagen. Denmark. Slides.
Formal Haagerup standard form on infinite index morphisms of factors. Groups, Operators, and Banach Algebras Webinar. Lancaster University. UK. Slides.
Internal categories of factors. Zagreb Workshop on Operator Theory. University of Zagreb. Zagreb, Croatia. Slides. Video.
Formal Haagerup standard form on infinite index morphisms of factors. Canadian Operator Symposium, Fields Institute, Canada. Slides
Globularly generated double categories. Extending functors and filling squares. [In Spanish] UAM-I. Slides

Activities

Past activities

List of past activities

Books, papers, etc.

Bookshelf

Resources

Resources in applied category theory