Related papers: Injective types in univalent mathematics

We determine a necessary and sufficient condition for a polynomial over an algebraically closed field $k$ to induce a surjective map on matrix algebras $M_n(k)$ for $n \ge 2$. The criterion is given in terms of critical points and uses…

The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…

In this paper, we introduce the notion of relative ultragraph algebras and extend classical injectivity criteria for representations, particularly those arising from branching systems,to this relative setting. This new concept is closely…

We study permutation-invariant embeddings of $d$-dimensional point sets, which are defined by sorting $D$ independent one-dimensional projections of the input. Such embeddings arise in graph deep learning where outputs should be invariant…

In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…

We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that there exists a monad T such that a morphism of topological spaces admits T-algebra structure…

Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…

For an endomorphism s of R with s^{t}=1 we prove that the truncated polynomial ring (algebra) R[w,s]/(w^{t}) embeds into M_{t}(R[z]/(z^{t})). For an involution we exhibit an embedding of R into M_{2,1}^{s}(R), where M_{2,1}^{s}(R) is the…

We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup…

We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…

A noncommutative projective variety is defined, after Artin and Zhang, by a graded coherent algebra A, where the category of coherent sheaves is the quotient qgr(A) of the category of finitely presented graded modules by the subcategory of…

We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…

We investigate predicative aspects of order theory in constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky's propositional resizing axioms or excluded middle. Our work…

The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…

We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in…

We present a complex frame of eleven vectors in 4-space and prove that it defines injective measurements. That is, any rank-one $4\times 4$ Hermitian matrix is uniquely determined by its values as a Hermitian form on this collection of…

We study multidimensional configurations (infinite words) and subshifts of low pattern complexity using tools of algebraic geometry. We express the configuration as a multivariate formal power series over integers and investigate the setup…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…