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ACS
2007
13 years 5 months ago
Directed Algebraic Topology, Categories and Higher Categories
Directed Algebraic Topology is a recent field, deeply linked with Category Theory. A ‘directed space’ has directed homotopies (generally non reversible), directed homology gro...
Marco Grandis
DAGSTUHL
2006
13 years 6 months ago
Enriched categories and models for spaces of dipaths
Partially ordered sets, causets, partially ordered spaces and their local counterparts are now often used to model systems in computer science and theoretical physics. The order mo...
Timothy Porter
ACS
2011
12 years 11 months ago
Algebras of Higher Operads as Enriched Categories
Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin t...
Michael Batanin, Mark Weber
ACS
2010
13 years 5 months ago
Graded and Koszul Categories
Koszul algebras have arisen in many contexts; algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology. The aim of this paper and several sequel paper...
Roberto Martínez-Villa, Øyvind Solbe...
ACS
2006
13 years 5 months ago
Universality of Coproducts in Categories of Lax Algebras
Abstract. Categories of lax (T, V )-algebras are shown to have pullbackstable coproducts if T preserves inverse images. The general result not only gives a common proof of this pro...
Mojgan Mahmoudi, Christoph Schubert, Walter Tholen