Formalizing the∞-categorical Yoneda lemma

N Kudasov, E Riehl, J Weinberger - Proceedings of the 13th ACM …, 2024‏ - dl.acm.org
Formalized 1-category theory forms a core component of various libraries of mathematical
proofs. However, more sophisticated results in fields from algebraic topology to theoretical …

Qualitative Research From Grounded Theory to Build a Scientific Framework on the Researcher's Epistemic Competence

A Deroncele-Acosta, R Gross-Tur… - International …, 2024‏ - journals.sagepub.com
The Epistemic Competence of the Researcher is a critical success factor for ethical, rigorous,
and creative research performance, but it requires a deep epistemological and …

Univalent double categories

N Van Der Weide, N Rasekh, B Ahrens… - Proceedings of the 13th …, 2024‏ - dl.acm.org
Category theory is a branch of mathematics that provides a formal framework for
understanding the relationship between mathematical structures. To this end, a category not …

Insights From Univalent Foundations: A Case Study Using Double Categories

N Rasekh, N van der Weide, B Ahrens… - arxiv preprint arxiv …, 2024‏ - arxiv.org
Category theory unifies mathematical concepts, aiding comparisons across structures by
incorporating objects and morphisms, which capture their interactions. It has influenced …

Logical Aspects of Virtual Double Categories

H Nasu - arxiv preprint arxiv:2501.17869, 2025‏ - arxiv.org
This thesis deals with two main topics: virtual double categories as semantics environments
for predicate logic, and a syntactic presentation of virtual double categories as a type theory …

Bifibrations of polycategories and classical multiplicative linear logic

N Blanco - arxiv preprint arxiv:2305.15139, 2023‏ - arxiv.org
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying
how to express certain categorical structures as universal properties by generalising the …

Directed equality with dinaturality

A Laretto, F Loregian, N Veltri - arxiv preprint arxiv:2409.10237, 2024‏ - arxiv.org
We show how dinaturality plays a central role in the interpretation of directed type theory
where types are interpreted as (1-) categories and directed equality is represented by $\hom …

An Internal Logic of Virtual Double Categories

H Nasu - arxiv preprint arxiv:2410.06792, 2024‏ - arxiv.org
We present a type theory called fibrational virtual double type theory (FVDblTT) designed
specifically for formal category theory, which is a succinct reformulation of New and Licata's …

The Univalence Maxim and Univalent Double Categories

N Rasekh, N van der Weide, B Ahrens… - … Conference on Types …, 2024‏ - nmvdw.github.io
▶ Often mathematical structures are considered up to isomorphism rather than up to
equality▶ Examples: groups, rings, R-modules, vector spaces,...▶ Isomorphism implies …