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 …

Data structures for topologically sound higher-dimensional diagram rewriting

A Hadzihasanovic, D Kessler - arxiv preprint arxiv:2209.09509, 2022 - arxiv.org
We present a computational implementation of diagrammatic sets, a model of higher-
dimensional diagram rewriting that is" topologically sound": diagrams admit a functorial …

A type-theoretic approach to semistrict higher categories

A Rice - arxiv preprint arxiv:2502.17068, 2025 - arxiv.org
Weak $\infty $-categories are known to be more expressive than their strict counterparts, but
are more difficult to work with, as constructions in such a category involve the manipulation …

[PDF][PDF] Computing spaces in type theory

M Doré - 2023 - ora.ox.ac.uk
In this thesis, we develop multiple case studies computing with and in cubical type theory.
We begin by setting up a framework to compute with sets in the theorem prover Cubical …