We investigate categorical versions of algebraically closed (= pure) embeddings, existentially closed embeddings, and the like, in the context of locally presentable categories. The definitions of S. Fakir [Fa, 75], as well as some of his results, are revisited and extended. Related preservation theorems are obtained, and a new proof of the main result of Rosický, Adámek and Borceux ([RAB, 02])...

We determine the base space of the Kuranishi family of some complete intersection in the product of an abelian variety and a projective space. As a consequence we obtain new examples of obstructed irregular surfaces with ample canonical bundle and maximal Albanese dimension. Mathematics Subject Classification (2000): 13D10, 14D15.

We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general result, we present a purely algebraic proof of “étale implies exponentiable”, alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphi...

First, we briefly recall the main definitions of the theory of Information Bases and Translations. These mathematical structures are the basis to construct the cartesian closed category InfBas, which is equivalent to the category ScDom of Scott Domains. Then, we will show that all the definitions and the proof of all the properties that one needs in order to show that InfBas is indeed a cartesi...

A hica is a highest weight, homogeneous, indecomposable, Calabi-Yau category of dimension 0. A hica has length l if its objects have Loewy length l and smaller. We classify hicas of length ≤ 4, up to equivalence, and study their properties. Over a fixed field F , we prove that hicas of length 4 are in one-one correspondence with bipartite graphs. We prove that an algebra AΓ controlling the hica...

In this paper we have discussed the relations between Maximal ideal, Prime ideal and irreducible ideal in an incline R. Mathematics Subject Classification: 16D25, 16Y60

For quasianalytic Denjoy–Carleman differentiable function classes C where the weight sequence Q = (Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of C-mappings is cartesian closed in the sense that C(E,C(F,G)) ∼= C(E × F,G) for convenient vector spaces. Applications to manifolds of mappings are given: ...

Proofs of coherence in category theory, starting from Mac Lane’s original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting systems in general. This applies to coherence results that assert that a category is a preorder, i.e. that “all diagrams commute”. This note is about this analog...

The additivity theorem for comlicial dérivateurs is proved. Also, to any exact category in the sense of Quillen a K-theory space is associated. This K-theory is shown to satisfy the additivity, approximation and resolution theorems. CONTENTS 1. Introduzione 1 2. Chain complexes, homotopies, derived categories 3 2.1. Definition of the derived category 3 2.2. Homotopy pullbacks and homotopy pusho...