N ov 2 00 6 TOPOLOGICAL FUNCTORS AS FAMILIARLY - FIBRATIONS
نویسندگان
چکیده
In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topo-logical functor is similar to (but not the same) the existing notions in the literature (see [2] 7.3), and it aims at the same examples. In our sense, a (pre) topological functor is a functor that creates cartesian families. A topological functor is, in particular, a fibration, and our emphasis is put in this fact. introduction In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topo-logical functor is similar to (but not the same) the existing notions in the literature (see [2] 7.3), and it aims at the same examples. Recall that a (pre) fibration is a functor that creates cartesian arrows. In our sense, a pre-topological functor is a functor that creates cartesian families, and it is topological provided that these families compose. A topological functor is, in particular, a fibration, and our emphasis is put in this fact. We develop an adequate generalization utilizing cartesian families (instead of cartesian arrows) of the basic ideas of Grothendieck's theory of fibered categories.
منابع مشابه
ar X iv : m at h / 03 06 23 5 v 2 [ m at h . D G ] 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD
We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].
متن کاملar X iv : m at h . D G / 0 30 62 35 v 2 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY
We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].
متن کاملN ov 2 00 5 Cohomology of F 1 - schemes Anton
1 Belian categories 3 1.1 Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Diagram chase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Snake Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Delta functors . . . . . . . . . . . . . . . . . . . . ....
متن کاملT ] 7 O ct 2 00 4 Categorical non abelian cohomology , and the Schreier theory of groupoids
By regarding the classical non abelian cohomology of groups from a 2-dimensional categorical viewpoint, we are led to a non abelian cohomology of groupoids which continues to satisfy classification, interpretation and representation theorems generalizing the classical ones. This categorical approach is based on the fact that if groups are regarded as categories, then, on the one hand, crossed m...
متن کاملar X iv : m at h . Q A / 0 61 10 87 v 1 3 N ov 2 00 6 MODULAR FUNCTORS ARE DETERMINED BY THEIR GENUS ZERO DATA
We prove in this paper that the genus zero data of a modular functor determines the modular functor. We do this by establishing that the S-matrix in genus onewith one point labeled arbitrarily can be expressed in terms of the genus zero information and we give an explicit formula. We do not assume the modular functor in question has duality or is unitary, in order to establish this. CONTENTS
متن کامل