In the field of programming language semantics and concurrency theory, wide attention is paid to the so called name-passing calculi, i.e. formalisms where name generation and passing play a fundamental role. A prototypical example is provided by the π-calculus. The peculiarities of name passing required to refine existing theoretical models and to invent new ones, such as coalgebras over preshe...

The category CoalgΣ of coalgebras with respect to a (bounded) signature Σ is known to be locally finitely presentable (see [1]). We strenghten this result by showing that CoalgΣ even is a presheaf category. Moreover, we give a presentation of this category as the category of all algebras of some (many-sorted) signature (without any equations). Σ–coalgebras, i.e., coalgebras with respect to a po...

We consider Lie algebroids over algebraic spaces (in short we call it as a-spaces) by considering the sheaf of Lie-Rinehart algebras. discuss about properties universal enveloping algebroid U(OX,L) a L an a-space (X,OX). This is done sheafification presheaf algebras for review extent to which structure (over special resembles bialgebras. In sequel present version Poincare-Birkhoff-Witt theorem ...

Given a left Quillen presheaf of localized model structures, we study the homotopy limit model structure on the associated category of sections. We focus specifically on towers and fibered products (pullbacks) of model categories. As applications we consider Postnikov towers of model categories, chromatic towers of spectra and Bousfield arithmetic squares of spectra. For stable model categories...

We extend the topos-theoretic treatment given in previous papers [1, 2] of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, an...

We will give descriptions of u-singularities as we introduce the notion of t-topos theoretic entropies. The unifying methodology for a u-singularity is the universal mapping property of an inverse or direct limit. The qualitative, conceptual, and structural analyses of u-singularities are given in terms of inverse and direct limits of micro decompositions of a presheaf and coverings of an objec...

Cubical type theory provides a constructive justification of homotopy theory. A crucial ingredient cubical is path lifting operation which explained computationally by induction on the involving several non-canonical choices. We present in this article two canonicity results, both proved sconing argument: result, every natural number equal to numeral, even if we take away equations defining str...

We discuss the problem of characterizing the property of a Grothendieck topos to satisfy a given `geometric' invariant as a property of its sites of de nition, and indicate a set of general techniques for establishing such criteria. We then apply our methodologies to speci c invariants, notably including the property of a Grothendieck topos to be localic (resp. atomic, locally connected, equiva...

We introduce an operad which acts on the Gerstenhaber-Schack complex of a prestack as defined by Dinh Van and Lowen, in particular allows us to endow this with underlying $L_{\infty}$-structure. make use $\operatorname{Quilt}$ was used Hawkins order solve presheaf case. Due additional difficulty posed presence twists, we have fundamentally different way (even for presheaves) allow extension pre...