In the present paper, we study category-theoretic properties ofmonomorphisms in categories of log schemes. This study allows one to give a purely categorytheoretic reconstruction of the log scheme that gave rise to the category under consideration. We also obtain analogous results for categories of schemes of locally finite type over the ring of rational integers that are equipped with “archime...

The Graded Classification Conjecture states that the pointed $K_{0}^{\operatorname {gr}}$ -group is a complete invariant of Leavitt path algebras finite graphs when these are considered with their natural grading by $\mathbb {Z}$ . strong version this conjecture functor full and faithful on category graded homomorphisms modulo conjugations invertible elements zero components. We show for unital...

A locally connected topos is a Galois topos if the Galois objects generate the topos. We show that the full subcategory of Galois objects in any connected locally connected topos is an inversely 2-filtered 2-category, and as an application of the construction of 2-filtered bilimits of topoi, we show that every Galois topos has a point. introduction. Galois topoi (definition 1.5) arise in Grothe...

We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE. More generally we show that K1(W) of a Waldhausen category W with cylinders and a saturated class of weak equivalences agrees with K1(DW) of the associated right pointed derivator DW. Introduction For a long time there was an interest in defining a nice K-theory for triangulated categories ...

Does category representation change in the course of development? And if so, how and why? The current study attempted to answer these questions by examining category learning and category representation. In Experiment 1, 4-year-olds, 6-year-olds, and adults were trained with either a classification task or an inference task and their categorization performance and memory for items were tested. ...

The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact spaces and manifolds. The notion of exterior weak N-Sequivalences is given by exterior maps which induce isomorphisms on the k-th N-exterior homotopy groups πN k for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray locali...

This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal subfactor. We compute generic fusion rules Grothendieck ring Rep(PSL(2,q)), q prime-power, applying Verlinde-like formula on character table. then prove that this family rings R_q interpolates to all integers q>=2, providing (when not prime-power) first example infinite non group-like simple integral ri...