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Object-Free Definition of Categories

Marco Riccardi (2013)

Formalized Mathematics

Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties:...

Obstructions for deformations of complexes

Frauke M. Bleher, Ted Chinburg (2013)

Annales de l’institut Fourier

We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes of modules for a profinite group G over a complete local Noetherian ring A of positive residue characteristic.

Oka manifolds: From Oka to Stein and back

Franc Forstnerič (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...

On 0-homology of categorical at zero semigroups

Boris Novikov, Lyudmyla Polyakova (2009)

Open Mathematics

The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.

On ℤ/2ℤ-extensions of pointed fusion categories

Leonid Vainerman, Jean-Michel Vallin (2012)

Banach Center Publications

We give a classification of ℤ/2ℤ-graded fusion categories whose 0-component is a pointed fusion category. A number of concrete examples are considered.

On a certain generalization of spherical twists

Yukinobu Toda (2007)

Bulletin de la Société Mathématique de France

This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of ( 0 , - 2 ) -curves on threefolds, or deforming -objects introduced by D.Huybrechts and R.Thomas.

On a homology of algebras with unit

Jacek Dębecki (2014)

Annales Polonici Mathematici

We present a very general construction of a chain complex for an arbitrary (even non-associative and non-commutative) algebra with unit and with any topology over a field with a suitable topology. We prove that for the algebra of smooth functions on a smooth manifold with the weak topology the homology vector spaces of this chain complex coincide with the classical singular homology groups of the manifold with real coefficients. We also show that for an associative and commutative algebra with unit...

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