3 citations · 6 across the 10 of their papers we have counts for
10 papers
Computads with invertible generators for weak ω-categories
Thibaut Benjamin, Camil Champin, Ioannis Markakis
We extend the notion of computads for weak \(ω\)-categories to allow marking certain generators as invertible, and describe inductively the free \(ω\)-categories they generate. Thi…
A type theory for invertibility in weak -categories
Thibaut Benjamin, Camil Champin, Ioannis Markakis
We present a conservative extension ICaTT of the dependent type theory CaTT for weak -categories with a type witnessing coinductive invertibility of cells. This extension allows…
Beyond Eckmann-Hilton: Commutativity in Higher Categories
Thibaut Benjamin, Ioannis Markakis, Wilfred Offord +2
We show that in a weak globular -category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a h…
Naturality for higher-dimensional path types
Thibaut Benjamin, Ioannis Markakis, Wilfred Offord +2
We define a naturality construction for the operations of weak omega-categories, as a meta-operation in a dependent type theory. Our construction has a geometrical motivation as a…
Invertible cells in -categories
Thibaut Benjamin, Ioannis Markakis
We study coinductive invertibility of cells in weak -categories. We use the inductive presentation of weak -categories via an adjunction with the category of computads, and s…
CaTT contexts are finite computads
Thibaut Benjamin, Ioannis Markakis, Chiara Sarti
Two novel descriptions of weak ω-categories have been recently proposed, using type-theoretic ideas. The first one is the dependent type theory CaTT whose models are ω-categories.…
Hom -categories of a computad are free
Thibaut Benjamin, Ioannis Markakis
We provide a new description of the hom functor on weak -categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom fun…
Computads for generalised signatures
Ioannis Markakis
We introduce a notion of signature whose sorts form a direct category, and study computads for such signatures. Algebras for such a signature are presheaves with an interpretation…
Computads for weak -categories as an inductive type
Christopher J. Dean, Eric Finster, Ioannis Markakis +2
We give a new description of computads for weak globular -categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads,…
Computing minimal generating systems for some special toric ideals
Dimitrios I. Dais, Ioannis Markakis
Let be the projective toric surface associated to a lattice polytope . If the number of lattice points lying on the boundary of is at least , it is known that $X_…