共查询到20条相似文献,搜索用时 0 毫秒
1.
Nicola Gambino 《Journal of Pure and Applied Algebra》2010,214(7):1193-1199
By combining ideas of homotopical algebra and of enriched category theory, we explain how two classical formulas for homotopy colimits, one arising from the work of Quillen and one arising from the work of Bousfield and Kan, are instances of general formulas for the derived functor of the weighted colimit functor. 相似文献
2.
Manfred Stelzer 《Journal of Pure and Applied Algebra》2019,223(6):2455-2473
We construct a combinatorical monoidal model category on simplicial flat cocommutative coalgebras over a Prüfer domain. The cofibrations are the morphisms which are pure as module maps. 相似文献
3.
Auslander-Reiten triangles and quivers are introduced into algebraic
topology.
It is proved that the existence of Auslander-Reiten triangles characterizes Poincaré
duality spaces, and that the Auslander-Reiten quiver is a weak
homotopy invariant.
The theory is applied to spheres whose Auslander-Reiten triangles and quivers are
computed. The Auslander-Reiten quiver over the $d$-dimensional sphere turns out to
consist of $d-1$ copies of ${\mathbb Z} A_{\infty}$. Hence the quiver is a
sufficiently sensitive invariant to tell spheres of different
dimension apart. 相似文献
4.
A variant of the trace in a monoidal category is given in the setting of closed monoidal derivators, which is applicable to endomorphisms of fiberwise dualizable objects. Functoriality of this trace is established. As an application, an explicit formula is deduced for the trace of the homotopy colimit of endomorphisms over finite categories in which all endomorphisms are invertible. This result can be seen as a generalization of the additivity of traces in monoidal categories with a compatible triangulation. 相似文献
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6.
M. Barot 《Journal of Pure and Applied Algebra》2008,212(1):33-46
For the cluster category of a hereditary or a canonical algebra, or equivalently for the cluster category of the hereditary category of coherent sheaves on a weighted projective line, we study the Grothendieck group with respect to an admissible triangulated structure. 相似文献
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8.
Crossed modules have longstanding uses in homotopy theory and the cohomology of groups. The corresponding notion in the setting of categorical groups, that is, categorical crosses modules, allowed the development of a low-dimensional categorical group cohomology. Now, its relevance is also shown here to homotopy types by associating, to any pointed CW-complex (X,∗), a categorical crossed module that algebraically represents the homotopy 3-type of X. 相似文献
9.
In this paper, when G is the circle S1 and M is a G-space, we study the rational homotopy type of the fixed point set MG, the homotopy fixed point set MhG, and the natural injection MG→MhG. 相似文献
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11.
Julia E. Bergner 《Topology》2007,46(4):397-436
Given any model category, or more generally any category with weak equivalences, its simplicial localization is a simplicial category which can rightfully be called the “homotopy theory” of the model category. There is a model category structure on the category of simplicial categories, so taking its simplicial localization yields a “homotopy theory of homotopy theories”. In this paper we show that there are two different categories of diagrams of simplicial sets, each equipped with an appropriate definition of weak equivalence, such that the resulting homotopy theories are each equivalent to the homotopy theory arising from the model category structure on simplicial categories. Thus, any of these three categories with the respective weak equivalences could be considered a model for the homotopy theory of homotopy theories. One of them in particular, Rezk’s complete Segal space model category structure on the category of simplicial spaces, is much more convenient from the perspective of making calculations and therefore obtaining information about a given homotopy theory. 相似文献
12.
Peter Jørgensen 《Advances in Mathematics》2005,193(1):223-232
The homotopy category of complexes of projective left-modules over any reasonably nice ring is proved to be a compactly generated triangulated category, and a duality is given between its subcategory of compact objects and the finite derived category of right-modules. 相似文献
13.
Muriel Livernet 《manuscripta mathematica》1998,96(3):295-315
We construct a non-commutative rational homotopy theory by replacing the pair (Lie algebras, commutative algebras) by the
pair (Leibniz algebras, Leibniz-dual algebras). Both pairs are Koszul dual in the sense of operads (Ginzburg–Kapranov). We
prove the existence of minimal models and the Hurewicz theorem in this framework. We define Leibniz spheres and prove that
their homotopy is periodic.
Received: 19 September 1997 / Revised version: 23 February 1998 相似文献
14.
The fundamental example of Gerstenhaber algebra is the space Tpoly(Rd) of polyvector fields on Rd, equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping G∞ algebra of a Gerstenhaber algebra G. This structure gives us a definition of the Chevalley-Harrison cohomology operator for G. We finally show the nontriviality of a Chevalley-Harrison cohomology group for a natural Gerstenhaber subalgebra in Tpoly(Rd). 相似文献
15.
We develop an obstruction theory for homotopy of homomorphisms between minimal differential graded algebras. We assume that has an obstruction decomposition given by and that f and g are homotopic on . An obstruction is then obtained as a vector space homomorphism . We investigate the relationship between the condition that f and g are homotopic and the condition that the obstruction is zero. The obstruction theory is then applied to study the set of homotopy classes . This enables us to give a fairly complete answer to a conjecture of Copeland-Shar on the size of the homotopy set [A,B] whenA and B are rational spaces. In addition, we give examples of minimal algebras (and hence of rational spaces) that have few homotopy classes of self-maps. Received February 22, 1999; in final form July 7, 1999 / Published online September 14, 2000 相似文献
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We answer a question of Blumberg, Cohen and Teleman, showing that the Chas–Sullivan loop homology is the Hochschild cohomology of any object in the rational string topology category of a compact, simply connected, Lie group G. Moreover, we show that the answer follows from the classification of the localizing subcategories of the derived category of chains on the based loops of G, which we achieve using the stratification machinery of Benson, Iyengar and Krause. For integral coefficients we get similar results for G a simply-connected special unitary group. 相似文献
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19.
Luca Moci 《Journal of Pure and Applied Algebra》2011,215(8):1980-1989
20.
Hans-Joachim Baues 《Journal of Pure and Applied Algebra》2007,211(3):821-850
We develop the obstruction theory of the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations by using the cohomology of categories. The obstructions are defined in Baues-Wirsching cohomology groups. We introduce translation cohomology to classify endomorphisms in the 2-category of abelian track categories. In a sequel to this paper we will show, under certain conditions which are satisfied by all homotopy categories, that a translation cohomology class determines the exact triangles of a triangulated category. 相似文献