Locally finitely presentable categories are known to be precisely the categories of models of essentially algebraic theories, i.e., categories of partial algebras whose domains of definition are determined by equations in total operations. Here we show an analogous description of locally finitely multipresentable categories. We also prove that locally finitely multipresentable categories are pr...

We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as potential yoga for dealing with processes and processes of processes. Introduction There does seem to be a problem in neuroscience in finding a language suitable for describing brain activity in a way which could lead to deduc...

This paper is a contribution to the presentation of fractal sets in terms of final coalgebras. The first result on this topic was Freyd’s Theorem: the unit interval [0, 1] is the final coalgebra of a functor X 7→ X ⊕ X on the category of bipointed sets. Leinster [L] offers a sweeping generalization of this result. He is able to represent many of what would be intuitively called self-similar spa...

We show that there is no triangulation of the infinite real Grassmannian G(k, R∞) nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of G(k, R∞) subdividing the matroid stratification. This is proved by an argument in projective geometry, considering a specific sequence of configurations of points in the plane. The Grassmannian G...

We show that there is no triangulation of the infinite real Grassmannian G(k,R∞) nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of G(k,R∞) subdividing the matroid stratification. This is proved by an argument in projective geometry, considering a specific sequence of configurations of points in the plane. The Grassmannian G(k...

Let T (j) be the dual of the jth stable summand of Ω2S3 (at the prime 2) with top class in dimension j. Then it is known that T (j) is a retract of a suspension spectrum, and that the homotopy colimit of a certain sequence T (j) → T (2j) → . . . is an infinite wedge of stable summands of K(V, 1)’s, where V denotes an elementary abelian 2 group. In particular, when one starts with T (1), one get...

To the memory of my father. Abstract The classical Eckmann-Hilton argument shows that two monoid structures on a set, such that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is commutative. This argument immediately gives a proof of the commutativity of the higher homotopy groups. A reformulation of this argument in the language of higher categories is: suppo...

Abstract Given a marked $$\infty $$ ∞ -category $$\mathcal {D}^{\dagger }$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">D† (i.e. an equipped with specified collection of morphisms) and functor $$F: \mathcal {D}\rightarrow ...

Modular speciications: constructions with nite colimits, diagrams, isomorphisms Catherine ORIAT R esum e : La composition de sp eciications modulaires peut ^ etre mod elis ee, dans le forma-lisme des cat egories, par des colimites de diagrammes. Les sommes amalgam ees permettent en particulier de d ecrire l'assemblage de deux sp eciications qui ont une partie commune. Ce travail etend cette id ...

The influence of irradiance and iron (Fe) supply on phytoplankton processes was investigated, north (47øS, 142øE) and south (54øS, 142øE) of the Subantarctic Front in austral autumn (March 1998). At both sites, resident cells exhibited nutrient stress (Fv/ F m < 0.3). Shipboard perturbation experiments examined two light (mean in situ and elevated) and two Fe (nominally 0.5 and 3 nM) treatments...