This thesis introduces the concept of visual subcategories. Many image understanding tasks such as object detection and image classification are formulated as binary classification problems, where the positive examples are instances (bounding boxes or images) of a specific object or scene category, and negative examples are background patches or images. Due to large intra-class variation in the...

We define A∞-bimodules similarly to Tradler and show that this notion is equivalent to an A∞-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground commutative ring. Serre A∞-functors are defined via A∞-bimodules likewise Kontsevich and Soibelman. We prove that a unital closed under shifts A∞-category A over a field k adm...

We define A∞-bimodules similarly to Tradler and show that this notion is equivalent to an A∞-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground commutative ring. Serre A∞-functors are defined via A∞-bimodules likewise Kontsevich and Soibelman. We prove that a unital closed under shifts A∞-category A over a field k adm...

We prove in this paper a noncommutative version of Leray Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with E 2 terms as E 2 p,q = HP p (A; HP q (B, A)) =⇒ HP p+q (B) and E 2 p,q = HP p (A; Kq(B, A)) =⇒ Kp+q(B).

We prove in this paper a noncommutative version of Leray Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with E terms as Ep,q = HPp(A; HPq(B,A)) =⇒ HPp+q(B) and Ep,q = HPp(A; Kq(B,A)) =⇒ Kp+q(B).

Martin Sleziak HAD-classes in epireflective subcategories of Top Introduction Heredity of AD-classes References Basic definitions Hereditary coreflective subcategories of Top A generalization – epireflective subcategories AD-classes and HAD-classes Subcategories of Top All subcategories are assumed to be full and isomorphism-closed. subcategory of Top = class of topological spaces closer under ...

We introduce in this paper the notion of noncommutative Serre fibration (shortly, NCSF) and show that up to homotopy, every NCCW complex morphism is some noncommutative Serre fibration. We then deduce a six-term exact sequence for the periodic cyclic homology and for K-theory of an arbitrary noncommutative Serre fibration. We also show how to use this technique to compute K-theory and cyclic th...