The notion of a simplicial set originated in algebraic topology and has also been utilized extensively category theory, but until relatively recently was not used outside those fields. However, with the increasing prominence higher categorical methods wide range applications, it is important for researchers fields to have good working knowledge them. This paper intended as an introduction sets,...

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...

In a series of publications in the early 1990s, L D Nel set up a study of non-normable topological vector spaces based on methods in category theory. One of the important results showed that the classical operations of derivative and integral in Calculus can in fact be obtained by a rather simple construction in categories. Here we present this result in a concise form. It is important to note ...

A first order representation (fo.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and...

We present a design framework for small-satellite systems that ensures that (1) each satellite has a consistent theory to infer new information from information it perceives and (2) the theory for the entire system is consistent so that a satellite can infer new information from information communicated to it. This research contributes to our Reliable and Formal Design (RFD) process, which stri...