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A characterization of Ext(G,ℤ) assuming (V = L)

Saharon Shelah, Lutz Strüngmann (2007)

Fundamenta Mathematicae

We complete the characterization of Ext(G,ℤ) for any torsion-free abelian group G assuming Gödel’s axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in (V = L) that, for a singular cardinal ν of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence ( ν p : p ∈ Π ) of cardinals satisfying ν p ≤ 2 ν (where Π is the set of all primes), there is a torsion-free abelian group G of size ν such that ν p equals the p-rank of Ext(G,ℤ) for every...

A Chen model for mapping spaces and the surface product

Grégory Ginot, Thomas Tradler, Mahmoud Zeinalian (2010)

Annales scientifiques de l'École Normale Supérieure

We develop a machinery of Chen iterated integrals for higher Hochschild complexes. These are complexes whose differentials are modeled on an arbitrary simplicial set much in the same way the ordinary Hochschild differential is modeled on the circle. We use these to give algebraic models for general mapping spaces and define and study the surface product operation on the homology of mapping spaces of surfaces of all genera into a manifold. This is an analogue of the loop product in string topology....

A classification of small homotopy functors from spectra to spectra

Boris Chorny (2016)

Fundamenta Mathematicae

We show that every small homotopy functor from spectra to spectra is weakly equivalent to a filtered colimit of representable functors represented in cofibrant spectra. Moreover, we present this classification as a Quillen equivalence of the category of small functors from spectra to spectra equipped with the homotopy model structure and the opposite of the pro-category of spectra with the strict model structure.

A coalgebraic semantics of subtyping

Erik Poll (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.

A Coalgebraic Semantics of Subtyping

Erik Poll (2010)

RAIRO - Theoretical Informatics and Applications

Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.

A coalgebraic view on reachability

Thorsten Wißmann, Stefan Milius, Shin-ya Katsumata, Jérémy Dubut (2019)

Commentationes Mathematicae Universitatis Carolinae

Coalgebras for an endofunctor provide a category theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra...

A cohomology theory for colored tangles

Carmen Caprau (2014)

Banach Center Publications

We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labeled by irreducible representations of U q ( s l ( 2 ) ) . We show that the corresponding colored invariants of tangles can be assembled into invariants of bigger tangles. For the case of knots and links, the corresponding theory is a categorification of the colored Jones polynomial, and provides a tool for efficient computations of the resulting colored invariant of knots and links. Our theory is...

A construction of simplicial objects

Tomáš Crhák (2001)

Commentationes Mathematicae Universitatis Carolinae

We construct a simplicial locally convex algebra, whose weak dual is the standard cosimplicial topological space. The construction is carried out in a purely categorical way, so that it can be used to construct (co)simplicial objects in a variety of categories --- in particular, the standard cosimplicial topological space can be produced.

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