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Formalizing the∞-categorical Yoneda lemma
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 …
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
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 …
and creative research performance, but it requires a deep epistemological and …
Univalent double categories
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 …
understanding the relationship between mathematical structures. To this end, a category not …
Insights From Univalent Foundations: A Case Study Using Double Categories
Category theory unifies mathematical concepts, aiding comparisons across structures by
incorporating objects and morphisms, which capture their interactions. It has influenced …
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 …
for predicate logic, and a syntactic presentation of virtual double categories as a type theory …
Bifibrations of polycategories and classical multiplicative linear logic
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 …
how to express certain categorical structures as universal properties by generalising the …
Directed equality with dinaturality
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 …
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 …
specifically for formal category theory, which is a succinct reformulation of New and Licata's …
The Univalence Maxim and Univalent Double Categories
▶ Often mathematical structures are considered up to isomorphism rather than up to
equality▶ Examples: groups, rings, R-modules, vector spaces,...▶ Isomorphism implies …
equality▶ Examples: groups, rings, R-modules, vector spaces,...▶ Isomorphism implies …