A categorical and Łukasiewicz-Topos framework for Łukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Łukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generaliz...

In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the...

We present a constructive algebraic integration theory. The theory is constructive in the sense of Bishop, however we avoid the axiom of countable, or dependent, choice. Thus our results can be interpreted in any topos. Since we avoid impredicative methods the results may also be interpreted in Martin-L type theory or in a predicative topos in the sense of Moerdijk and Palmgren. We outline how ...

A quantum picture of the causal structure of Minkowski space M is presented. The mathematical model employed to this end is a nonclassical version of the classical topos {H} of real quaternion algebras used elsewhere to organize the perceptions of spacetime events of a Boolean observer into M. Certain key properties of this new quantum topos are highlighted by contrast against the corresponding...

This article focuses on the presence and treatment of sound in killing adversary Arthurian novel. We begin by establishing a definition topos, based large list occurrences, which leads us to see death enemy variation larger more widespread motif. then study evolution this topos from epic texts latest novels. Finally, we notice significance these sounds family romances authors seem seek perpetua...

Moerdijk’s site description for equivariant sheaf toposes on open topological groupoids is used to give a proof for the (known, but apparently unpublished) proposition that if H is a subgroupoid of an open topological groupoid G , then the topos of equivariant sheaves on H is a subtopos of the topos of equivariant sheaves on G . This proposition is then applied to the study of quotient geometri...

— We present hère some facts about recursive function theory that we describe in an abstract jorm; for this we use hère fibered catégories. A first approach ofthis was made by P. Mulry by using of topos theory. Out of the results find hère, we give the first steps towards the treatment of partiality in an abstract form. Résumé. — Nous donnons ici quelques résultats sur les fonctions récursives ...