Proof nets for MLL, unit-free Multiplicative Linear Logic (Girard, 1987), provide elegant, abstract representations of proofs. Cut-free MLL proof nets form a category, under path composition, in the manner of EilenbergKelly-Mac Lane graphs (Eilenberg and Kelly, 1966; Kelly and Mac Lane, 1971). Objects are formulas of MLL, and a morphism A → B, a proof net from A to B, is a linking or matching b...

We introduce in this paper the notions of noncommutative (shortly, NC) CW-complex, noncommutative Serre fibration and show that up to homo-topy, every NC CW-complex algebra morphism is some noncommutative Serre fibration. We then deduce a six-term exact sequence for the periodic cyclic homology and for K-theory of an arbitrary noncommutative Serre fi-bration, or of a morphism in the category of...

Let CD be the category of all continuous domains and all mappings which preserve directed sups and the way-below relation. That is, a mapping f : P → Q is a morphism of CD if and only if f(sup D) = sup f(D) for any directed set D ⊂ P and f(x) œ f(y) if x œ y for any x, y ∈ P . We shall prove that the category CD is cartesian closed. 1991 Mathematics Subject Classification 06B35.

This note establishes internal criteria on a category C and a separator 2 in C which characterize the condition that the 2-induced covariant hom-functor /i2: C -> Set is (epi, mono-source)-topological. Introduction. Hoffmann [4] showed how topological functors (of Herrlich [2]) may be recovered from factorizations of sources and sinks in the domain category. This process was extended to (F, M)-...

Let C be a small category and Set the category of sets. We define a C-set to be a functor Ω : C → Set. Thus Ω is simply a diagram of sets, the diagram having the same shape as C: for each object x of C there is specified a set Ω(x) and for each morphism α : x → y there is a mapping of sets Ω(α) : Ω(x) → Ω(y). If C happens to be a group (a category with one object and morphism set G) then a C-se...

A point process on a space is random bag of elements that space. In this paper we explore programming with processes in monadic style. To end identify X probability measures bags X. We describe view using the composition Giry and monads category measurable spaces functions prove also forms monad distributive law for monads. Finally, define morphism from to its intensity measure, show morphism. ...

Proof nets for MLL, unit-free Multiplicative Linear Logic (Girard, 1987), provide elegant, abstract representations of proofs. Cut-free MLL proof nets form a category, under path composition, in the manner of EilenbergKelly-Mac Lane graphs (Eilenberg and Kelly, 1966; Kelly and Mac Lane, 1971). Objects are formulas of MLL, and a morphism A → B, a proof net from A to B, is a linking or matching b...

This thesis is concerned with the definition and the study of properties of homotopic Hopf-Galois extensions in the category Ch 0 k of chain complexes over a field k, equipped with its projective model structure. Given a differential graded k-Hopf algebra H of finite type, we define a homotopic H-Hopf-Galois extension to be a morphism ' : B ! A of augmented H-comodule dg-k-algebras, where B is ...

Fix a morphism of schemes f : X → S which is flat, proper, and “fiber-by-fiber semi-stable”. Let IV LS be the functor on the category of log schemes over S which to any T associates the isomorphism classes of pairs (MX , f), where MX is a log structure on X×S T and f : pr∗ 2MT →MX is a morphism of log structures making (X×S T ,MX)→ T a log smooth, integral, and vertical morphism. The main resul...

For a given Galois structure on a category C and an eeective descent morphism p : E !B in C we describe the category of so-called weakly split objects over (E; p) in terms of internal actions of the Galois (pre)groupoid of (E; p) with an additional structure. We explain that this generates various known results in categorical Galois theory and in particular two results of M. Barr and R. Diacone...