In analogy with the classical theory of filters, for finitely complete categories, we provide the concepts of filter, G-neighborhood (short for \Grothendieck-neighborhood") and cover-neighborhood of a point, with the aim of studying convergence, cluster point and closure of sieves on objects of that kind of categories.

Abstract Many results about statistical convergence in a general setting can be derived by consideration of the convergence free space of null sequences and its related cofilter and filter. We derive… Expand

The notion of I-convergence was introduced in the paper [18]. This notion includes the notion of the statistical convergence which has been intensively investigated in last twenty years. In the… Expand

homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,… Expand