Related papers: Naturality for higher-dimensional path types
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
Classical definitions of weak higher-dimensional categories are given inductively; for example, a bicategory has a set of objects and hom categories, and a tricategory has a set of objects and hom bicategories. However, more recent…
We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming,…
This work contributes to clarifying several relationships between certain higher categorical structures and the homotopy types of their classifying spaces. Double categories (Ehresmann, 1963) have well-understood geometric realizations, and…
Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the "synthetic" development of homotopy…
Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…
Batanin and Leinster's work on globular operads has provided one of many potential defnitions of a weak $\omega$-category. Through the language of globular operads they construct a monad whose algebras encode weak $\omega$-categories. The…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
We show that the nerve of a strict omega-category can be described algebraically as a simplicial set with additional operations subject to certain identities. The resulting structures are called sets with complicial identities. We also…
Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key mathematical disciplines, notably homotopy…
We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…
Agda is a dependently-typed functional programming language, based on an extension of intuitionistic Martin-L\"of type theory. We implement first order natural deduction in Agda. We use Agda's type checker to verify the correctness of…
We state a construction theorem for specifications starting from single-site conditional probabilities (singleton part). We consider general single-site spaces and kernels that are absolutely continuous with respect to a chosen product…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…
We prove a general version of the homological perturbation lemma which works in the presence of curvature, and without the restriction to strong deformation retracts, building on work of Markl. A key observation is that the notion of strong…
In this paper we consider composition operators on locally convex spaces of functions defined on $\mathbb{R}$. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the strong…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…