Some Pre-filters in EQ-Algebras

In this paper, the notion of an obstinate prefilter (filter) in an EQ-algebra ξ is introduced and a characterization of it is obtained by some theorems. Then the notion of maximal prefilter is defined and is characterized under some conditions. Finally, the relations among obstinate, prime, maximal, implicative and positive implicative prefilters are studied

On the Category of EQ-algebras

In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculated coproduct and pushout in a special case. Also, we constructed a free EQ-algebra on a singleton

Characterizations of Some Fuzzy Prefilters (Filters) in E

We introduce and study some types of fuzzy prefilters (filters) in EQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters (filters). Next, using their characterizations, we mainly consider the relationships among these special fuzzy filters. Particularly, we find some conditions under which a fuzzy implicative prefilter (filter) is equivalent to a fuzzy positive implicative prefilter (filter). As applications, we obtain some new results about classical filters in EQ-algebras and some related results about fuzzy filters in residuated lattices

nn-Fold Filters of EQ-Algebras

In this paper, we apply the notion of $n$-fold filters to the $EQ$-algebras and introduce the concepts of $n$-fold pseudo implicative, $n$-fold implicative, $n$-fold obstinate, $n$-fold fantastic prefilters and filters on an $EQ$-algebra $\mathcal{E}$. Then we investigate some properties and relations among them. We prove that the quotient algebra $\mathcal{E}/F$ modulo an 1-fold pseudo implicative filter of an $EQ$-algebra $\mathcal{E}$ is a good $EQ$-algebra and the quotient algebra $\mathcal{E}/F$ modulo an 1-fold fantastic filter of a good $EQ$-algebra $\mathcal{E}$ is an $IEQ$-algebra

Quantisation of derived Poisson structures

We prove that every $0$-shifted Poisson structure on a derived Artin $n$-stack admits a curved $A_{\infty}$ quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes. Where the Kontsevich-Tamarkin approach to quantisation hinges on invariance of the Hochschild complex under affine transformations, we instead exploit the observation that it carries an anti-involution, and that such anti-involutive deformations of the complex of polyvectors are essentially unique.Comment: 27 pp; v2 argument simplified and Artin section removed; v3 added long section extending to Artin n-stacks via differential operator