Categories of lax (T, V )-algebras are shown to have pullbackstable coproducts if T preserves inverse images. The general result not only gives a common proof of this property in many topological categories but also shows that important topological categories, like the category of uniform spaces, are not presentable as a category of lax (T, V )-algebras, with T preserving inverse images. Moreov...

If T is a (first order) universal theory then we can consider the category of existentially closed models of T with embeddings as morphisms. This class of structures is in general not the class of models of a first order theory T ′. (It will be, just if T has a model companion T ′.) The “model theory” of such a “non-elementary class” was a substantial line of research in the 1970’s, mainly amon...

We present a comparative study of certain invariants defined for group actions and their analogues orbifolds. In particular, we prove that Fadell's equivariant category $G$-spaces coincides with the Lusternik-Schnirelmann orbifolds when is finite.

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we obtain a functor which “approximates” objects from the module category of the endomorphism algebra of C in T . This generalises and extends a construction of Jør...

For a relative exact homological category (C,E), we define relative points over an arbitrary object in C, and show that they form an exact homological category. In particular, it follows that the full subcategory of nilpotent objects in an exact homological category is an exact homological category. These nilpotent objects are defined with respect to a Birkhoff subcategory in C as defined by T....

The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)]. That looks like a composite resolution; first an algebra is resolved by means of free modules (over the ground ring) and then this resolution is given the structure of a DG-algebra and resolved by the ...

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg–Moore category CT that represents bimorphisms. The category of actions in CT is then shown to be monadic over the base category C.

Abstract This paper is a sequel to T-structures and twisted complexes on derived injectives by the same author with W. Lowen M. Van den Bergh. We define dg-category of unbounded dg-category, which particularly interesting in case dg-categories or projectives associated t-structure. On such we natural “injective” dually “projective” intended as direct generalization homotopy categories injective...

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg–Moore category CT that represents bimorphisms. The category of actions in CT is then shown to be monadic over the base category C.