Results 1 
7 of
7
TRIPLES, ALGEBRAS AND COHOMOLOGY
 REPRINTS IN THEORY AND APPLICATIONS OF CATEGORIES
, 2003
"... ..."
New Model Categories From Old
 J. Pure Appl. Algebra
, 1995
"... . We review Quillen's concept of a model category as the proper setting for defining derived functors in nonabelian settings, explain how one can transport a model structure from one category to another by mean of adjoint functors (under suitable assumptions), and define such structures for categor ..."
Abstract

Cited by 13 (5 self)
 Add to MetaCart
. We review Quillen's concept of a model category as the proper setting for defining derived functors in nonabelian settings, explain how one can transport a model structure from one category to another by mean of adjoint functors (under suitable assumptions), and define such structures for categories of cosimplicial coalgebras. 1. Introduction Model categories, first introduced by Quillen in [Q1], have proved useful in a number of areas  most notably in his treatment of rational homotopy in [Q2], and in defining homology and other derived functors in nonabelian categories (see [Q3]; also [BoF, BlS, DwHK, DwK, DwS, Goe, ScV]). From a homotopy theorist's point of view, one interesting example of such nonabelian derived functors is the E 2 term of the mod p unstable Adams spectral sequence of Bousfield and Kan. They identify this E 2 term as a sort of Ext in the category CA of unstable coalgebras over the mod p Steenrod algebra (see x7.4). The original purpose of this note w...
The bicategories of corings
 J. Pure Appl. Algebra
"... Abstract. To a Bcoring and a (B, A)bimodule that is finitely generated and projective as a right Amodule an Acoring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Abstract. To a Bcoring and a (B, A)bimodule that is finitely generated and projective as a right Amodule an Acoring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projective on one side, together with a map of corings over the same base ring, lead to the notion of a modulemorphism, which extends the notion of a morphism of corings (over different base rings). A modulemorphism of corings induces functors between the categories of comodules. These functors are termed pullback and pushout functors respectively and thus relate categories of comodules of different corings. We study when the pullback functor is fully faithful and when it is an equivalence. A generalised descent associated to a morphism of corings is introduced. We define a category of modulemorphisms, and show that pushout functors are naturally isomorphic to each other if and only if the corresponding modulemorphisms are mutually isomorphic. All these topics are studied within a unifying language of bicategories and the extensive
Homotopy Theory Of Modules And Gorenstein Rings
, 1998
"... Homotopy Categories [12], and Brown Representability Theorem is applicable. We note that our results on injective homotopy generalize some recent results of Jørgensen [25]. In Section 6, inspired from the construction of the stable homotopy category of spectra [32], we study the existence of a stabl ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Homotopy Categories [12], and Brown Representability Theorem is applicable. We note that our results on injective homotopy generalize some recent results of Jørgensen [25]. In Section 6, inspired from the construction of the stable homotopy category of spectra [32], we study the existence of a stable homotopy category associated to the projective or injective homotopy of a ring . Since the stable module categories are not in general triangulated, it is useful in many cases to replace them by their stabilizations [8], [19], which are triangulated categories, and this can be done in a universal way. We say that a ring has a projective, resp. injective, stable homotopy category if the stabilization of Mod(), resp. of Mod(), is compactly generated. We prove that in case is right Gorenstein in the sense of [8], and the ring is left coherent and right perfect or right Morita, then such a stable homotopy category exists and can be described as the triangulated stable category of CohenMacaula...
COHOMOLOGY FOR BICOMODULES. SEPARABLE AND MASCHKE FUNCTORS.
, 2006
"... Abstract. We introduce the category of bicomodules for a comonad in a Grothendieck category whose underlying functor is right exact and preserves direct sums. We characterize comonads with a separable forgetful functor by means of cohomology groups using cointegrations into bicomodules. We present t ..."
Abstract
 Add to MetaCart
Abstract. We introduce the category of bicomodules for a comonad in a Grothendieck category whose underlying functor is right exact and preserves direct sums. We characterize comonads with a separable forgetful functor by means of cohomology groups using cointegrations into bicomodules. We present two applications: the characterization of coseparable corings stated in [12], and the characterization of coseparable coalgebras coextensions stated in [17].
HOMOTOPICAL STRUCTURES IN CATEGORIES
, 2003
"... Abstract. In this paper is presented a new approach to the axiomatic homotopy theory in categories, which offers a simpler and more useful answer to this old question: how two objects in a category (without any topological feature) can be deformed each in other? 1. ..."
Abstract
 Add to MetaCart
Abstract. In this paper is presented a new approach to the axiomatic homotopy theory in categories, which offers a simpler and more useful answer to this old question: how two objects in a category (without any topological feature) can be deformed each in other? 1.
Submitted to ICFP’13 Unifying Recursion Schemes
"... Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent such ..."
Abstract
 Add to MetaCart
Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent such unifications are the ‘recursion schemes from comonads ’ of Uustalu, Vene and Pardo, and our own ‘adjoint folds’. Until now, these two unified schemes have appeared incompatible. We show that this appearance is illusory: in fact, adjoint folds subsume recursion schemes from comonads. The proof of this claim involves standard constructions in category theory that are nevertheless not well known in functional programming: EilenbergMoore categories and bialgebras. The link between the two schemes is provided by the fusion rule of categorical fixedpoint calculus.