If A is a small category and E a Grothendieck topos, the Kan extension LanF of a flat functor F : A → E along any functor A → D preserves whatever finite limits may exist in D; this is a well known fundamental result in topos theory. We shall present a metamathematical argument to derive out of this some other left exactness results, for Kan extensions with values in a (possibly large) site E. ...

‎In this paper we take $mathcal A$ to be the category {bf Pos-S}‎ ‎of $S$-posets‎, ‎for a posemigroup $S$‎, ${mathcal M}_{pd}$ to‎ ‎be the class of partially ordered sequantially-dense‎ ‎monomorphisms and study the categorical properties‎, ‎such as‎ ‎limits and colimits‎, ‎of this class‎. ‎These properties are usually‎ ‎needed to study the homological notions‎, ‎such as injectivity‎, ‎of‎ ‎$S$-...

Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined an “algebraic pattern”, which we mean ?-category equipped with a factorization system and collection of “elementary” objects. Examples that occur as such “Segal O-spaces” for pattern O include ?-categories, (?,n)-categories, ?-operads (including symmetric, non-symmetric, cyclic, modular ones),...

We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, nite sets of sentences, or theory extensions using unique-existential quantiiers, respectively. They faithfully represent theories, model categories, theory morphisms, colimit of theor...

Let G be a compact Lie group and p a fixed prime number. Recall that an elementary abelian p-group is an abelian group isomorphic to (Z/p) for some r. Jackowski and McClure showed in [10] how to decompose the classifying space BG at the prime p as a homotopy colimit of spaces of the form BCG(V ), where V is a nontrivial elementary abelian p-subgroup of G and CG(V ) is the centralizer of V in G ...

While aspect-oriented programming (AOP) addresses introduction of “aspects” at the code level, we argue that addressing this at the level of software architecture is conceptually more adequate, since many aspects, that is, “crosscutting concerns”, are formulated already in the requirements, and therefore can be dealt with in a more controlled manner in the “earlier” phase of software architectu...

Cognitive scientists of the embodied cognition tradition have been providing evidence that a large part of our creative reasoning and problemsolving processes are carried out by means of conceptual metaphor and blending, grounded on our bodily experience with the world. In this talk I shall aim at fleshing out a mathematical model that has been proposed in the last decades for expressing and ex...

This paper presents a technique by which solutions to reflexive domain equations can be found in a certain category of complete metric spaces. The objects in this category are the (non-empty) metric spaces and the arrows consist of two maps: an isometric embedding and a non-distance-increasing left inverse to it. The solution of the equation is constructed as a fixed point of a functor over thi...

This work contributes to clarifying several relationships between certain higher categorical structures and the homotopy type of their classifying spaces. Bicategories (in particular monoidal categories) have well understood simple geometric realizations, and we here deal with homotopy types represented by lax diagrams of bicategories, that is, lax functors to the tricategory of bicategories. I...

Anaerobic ammonia oxidation (anammox) as an important nitrogen loss pathway has been reported in marine oxygen minimum zones (OMZs), but the community composition and spatial distribution of anammox bacteria in the eastern tropical North Pacific (ETNP) OMZ are poorly determined. In this study, anammox bacterial communities in the OMZ off Costa Rica (CRD-OMZ) were analyzed based on both hydrazin...