Concept
Equivalence of categories
Related publications (38)
Cochains are all you need
In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...
EPFL2024Modal engineering of electromagnetic circuits to achieve rapid settling times
Inductive circuits and devices are ubiquitous and important design elements in many applications, such as magnetic drives, galvanometers, magnetic scanners, applying direct current (DC) magnetic fields to systems, radio frequency coils in nuclear magnetic ...
AIP Publishing2023Tunable biocomposite films fabricated using cellulose nanocrystals and additives for food packaging
Cellulose nanocrystals (CNCs) are considered a prospective packaging material to partially replace petroleumbased plastics attributed to their renewability, sustainability, biodegradability, and desirable attributes including transparency, oxygen, and oil ...
ELSEVIER SCI LTD2023Hopf algebras and Hopf-Galois extensions in infinity-categories
In this thesis, we study interactions between algebraic and coalgebraic structures in infinity-categories (more precisely, in the quasicategorical model of (infinity, 1)-categories). We define a notion of a Hopf algebra H in an E-2-monoidal infinity-catego ...
EPFL2022From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem
In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...
EPFL2022On minimal tilting complexes in highest weight categories
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie ...
2022Assessing Computational Thinking: Development and Validation of the Algorithmic Thinking Test for Adults
Olivier Lévêque, Cécile Hardebolle, Marc Lafuente Martinez
This study describes the development and validation process of a computational thinking (CT) test for adults. The team designed a set of items and explored a subset of those through two qualitative pilots. Then, in order to provide validity evidence based ...
2022Homotopical relations between 2-dimensional categories and their infinity-analogues
In this thesis, we study the homotopical relations of 2-categories, double categories, and their infinity-analogues. For this, we construct homotopy theories for the objects of interest, and show that there are homotopically full embeddings of 2-categories ...
EPFL2021Filter quotients and non-presentable (∞,1)-toposes
We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter quotient of the underlying elementary topos. We then specialize to the case of filter products of -ca ...
2021Aligning actions with objectives in endangered species recovery plans
To achieve conservation objectives for threatened and endangered species, managers must choose among potential recovery actions based on their efficacy. Yet, a lack of standardization in defining how conservation actions support recovery objectives can imp ...
WILEY2021