Related papers: Free differential modalities
We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…
We discuss free probability theory and free harmonic analysis from a categorical perspective. In order to do so, we extend first the set of analytic convolutions and operations and then show that the comonadic structure governing free…
Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to…
In monadic programming, datatypes are presented as free algebras, generated by data values, and by the algebraic operations and equations capturing some computational effects. These algebras are free in the sense that they satisfy just the…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces,…
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…
Interviews run on people, programs run on operating systems, voting schemes run on voters, games run on players. Each of these is an example of the abstraction pattern runs on matter. Pattern determines the decision tree that governs how a…
It often happens that free algebras for a given theory satisfy useful reasoning principles that are not preserved under homomorphisms of algebras, and hence need not hold in an arbitrary algebra. For instance, if $M$ is the free monoid on a…
Let H be an algebraic group scheme over a field k acting on a commutative k-algebra A which is a unique factorisation domain. We show that, under certain mild assumptions, the monoid of nonzero H-stable principal ideals in A is free…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We introduce the notion of pie algebra for a 2-monad, these bearing the same relationship to the flexible and semiflexible algebras as pie limits do to flexible and semiflexible ones. We see that in many cases, the pie algebras are…
We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids -- or in a straightforward generalisation, the…
We study the category of modules admitting compatible actions of the Lie algebra $\mathcal{V}$ of vector fields on an affine space and the algebra $\mathcal{A}$ of polynomial functions. We show that modules in this category which are…
We show that the infinite symmetric product of a connected graded-commutative algebra over the rationals is naturally isomorphic to the free graded-commutative algebra on the positive degree subspace of the original algebra. In particular,…
We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy…
Usually a name of the category is inherited from the name of objects. However more relevant for a category of objects and morphisms is an algebra of morphisms. Therefore we prefer to say a category of graphs if every morphism is a graph. In…
For any morphism of $\infty$-operads $\mathcal{P} \to \mathcal{O}$, we show that the free $\mathcal{O}$-algebra on a $\mathcal{P}$-algebra admits an explicit formula as the colimit over the $\mathcal{O}$-monoidal envelope of $\mathcal{P}$,…
In this paper we study algebras of modular forms on unitary groups of signature $(n,1)$. We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary we…