We introduce the notion of cumulants as applied to linear maps between associative (or commutative) algebras that are not compatible with algebraic product structure. These have a close relationship $$A_{\infty }$$ and $$C_{\infty morphisms, which classical homotopical tools for analyzing deformations algebraically maps. look at these two different perspectives understand how infinity-morphisms...

Injectivity of objects with respect to a set H of morphisms is an important concept of algebra and homotopy theory; here we study the logic of consequences of H, by which we understand morphisms h such that injectivity with respect to H implies injectivity with respect to h. We formulate three simple deduction rules for the injectivity logic and for its finitary version (where morphisms between...

In this work we shall consider some new result on the famous word problem called the Post Correspondence Problem (PCP), initially defined by E. Post. Halava, Hirvensalo and de Wolf [4] proved that the PCP is decidable if we assume that the morphisms are marked. Moreover, Halava, Harju and Hirvensalo [2] proved that even the generalized PCP is decidable in the case of marked morphisms. As a coro...

To say that C is a category with (functoral) multiplication means that there is a functor ⊗ : C → C called the multiplication where C is the category of pairs of objects and pairs of morphisms from C. [More technically, C is the category of functors and natural transformations from 2 to C where 2 is the category with objects 0 and 1, and the only morphisms are the identity morphisms.] Examples ...

We introduce partial Esakia morphisms, well partial Esakia morphisms, and strong partial Esakia morphisms between Esakia spaces and show that they provide the dual description of (∧,→) homomorphisms, (∧,→, 0) homomorphisms, and (∧,→,∨) homomorphisms between Heyting algebras, thus establishing a generalization of Esakia duality. This yields an algebraic characterization of Zakharyaschev’s subred...

Abstract We consider two preorder-enriched categories of ordered partial combinatory algebras: OPCA, where the arrows are functional (i.e., projective) morphisms, and OPCA † , applicative morphisms. show that has small products finite biproducts, coproducts, all in a suitable 2-categorical sense. On other hand, lacks nontrivial binary products. deduce from this pushout, over Set, realizability ...