We present a novel proof of Thomason’s theorem relating Bott inverted algebraic K-theory with finite coefficients and étale cohomology for smooth varieties over algebraically closed ground fields. Our proof involves first introducing a new theory, which we term algebraic K-homology, and proving it satisfies étale descent (with finite coefficients) on the category of normal, Cohen-Macaulay varie...

We present a database consisting of wood pile images, which can be used as a benchmark to evaluate the performance of wood pile detection and surveying algorithms. We distinguish six database categories which can be used for different types of algorithms. Images of real and synthetic scenes are provided, which consist of 7655 images divided into 354 data sets. Depending on the category the data...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...