We study the quadratic quotients of incidence category Young lattice defined by zero relations corresponding to adding two boxes same row, or column, both. show that last quotient corresponds Koszul dual original category, while first are, in a natural way, duals each other and hence they are particular self-dual. Both these known be basic representatives Morita equivalence class injections bet...

One can do the motivic homotopy theory in the context of different motivic homotopy categories. One can vary the topology on the category of schemes used to define the homotopy category or one can vary the category of schemes itself considering only schemes satisfying certain conditions. The category obtained by taking smooth schemes and the Nisnevich topology seems to play a distinguished role...

The aim of this paper is to define and study pointed and multi-pointed partition posets of type A and B (in the classification of Coxeter groups). We compute their characteristic polynomials, incidence Hopf algebras and homology groups. As a corollary, we show that some operads are Koszul over Z. Introduction For every finite Weyl group W , there exists a generalized partition poset (cf. [2]) d...

The notion of normal subobject having an intrinsic meaning in any protomodular category, we introduce the notion of normal functor, namely left exact conservative functor which reflects normal subobjects. The point is that for the category Gp of groups the change of base functors, with respect to the fibration of pointed objects, are not only conservative (this is the definition of a protomodul...

The cubical sets model of Homotopy Type Theory introduced by Bezem, Coquand and Huber [2] uses a particular category of presheaves. We show that this presheaf category is equivalent to a category of sets equipped with an action of a monoid of name substitutions for which a finite support property holds. That category is in turn isomorphic to a category of nominal sets [15] equipped with operati...

Making Iranian Schools Smart: From Policy to Practice E. Talaa’ee, Ph.D. N. Ansaari M. Pahlavaan Z. Abootaalebi To assess both the essence and ways of operationalization of a recently adopted policy by the MOE with the aim of making Iranian schools smart, four such schools were purposefully selected, observed, and questioned. The collected data have been analyzed using th...

RESPONSE THEORY MODELS Various polytomous IRT models parameterize the probability of response categories differently from each other. For example, the graded response model (GRM) (Samejima, 1969) is based on the cumulative log-odds principle, whereas the generalized partial credit model (GPCM) (Muraki, 1992) is based on the adjacent log-odds principle. It is widely known that these two polytomo...