Related papers: C-system of a module over a monad on sets

Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those…

We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.

Geometric folding processes are ubiquitous in natural systems ranging from protein biochemistry to patterns of insect wings and leaves. In a previous study, a folding operation between strings of formal languages was introduced as a model…

A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a…

Containers represent a wide class of type constructions relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the scope of dependently typed programming. When interpreting…

Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction…

People often refer to entities in an image in terms of their relationships with other entities. For example, "the black cat sitting under the table" refers to both a "black cat" entity and its relationship with another "table" entity.…

We present two logical systems based on dependent types that are comparable to ZFC, both in terms of simplicity and having natural set theoretic interpretations. Our perspective is that of a mathematician trained in classical logic, but…

A two-part report, containing (unrelated) essays on subobject classifiers and on monads.

Let B be the Lie algebra with basis {L_{i,j},C|i,j\in Z} and relations [L_{i,j},L_{k,l}]=((j+1)k-i(l+1))L_{i+k,j+l}+i\delta_{i,-k}\delta_{j+l,-2}C, [C,L_{i,j}]=0. It is proved that an irreducible highest weight B-module is quasifinite if…

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x]. Then C is R-finitely dominated, ie, homotopy equivalent over R to a bounded chain complex of finitely generated…

We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…

We present a framework for compositional program verification based on polynomial functors in dependent type theory. In this framework, polynomial functors serve as program interfaces, Kleisli morphisms for the free monad monad serve as…

Let $C \subset {\bf N}^d$ be an affine semigroup, and $R=K[C]$ its semigroup ring. This paper is a collection of various results on "$C$-graded" $R$-modules, especially, monomial ideals. For example, we show the following: If $R$ is normal…

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…

Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…

Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal category $\Cc$, and assume that $A$ is also a coalgebra, with a not-necessarily associative or unital left $B$-action. Then we can define a right $A$-action…

In this paper we develop an ideal structure theory for the class of left reductive regular semigroups and apply it to several subclasses of popular interest. In these classes we observe that the right ideal structure of the semigroup is…

Existential types are reconstructed in terms of small reflective subuniverses and dependent sums. The folklore decomposition detailed here gives rise to a particularly simple account of first-class modules as a mode of use of traditional…

Connections between heaps of modules and (affine) modules over rings are explored. This leads to explicit, often constructive, descriptions of some categorical constructions and properties that are implicit in universal algebra and…