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math.AT2026
Directed homological and cohomological operations
Eric Goubault
In this short note, we present a persistence module approach to directed cohomology, dual to the directed homology introduced by the author in a previous article. We lay out the fi…
math.AT2026
Homological algebra over non-unital rings and algebras, with applications to -categories
Eric Goubault, Eliot Médioni
The article is developing homological algebra in modules over non-unital rings and algebras. The main application is the definition and study of (directed) homology of …
math.AT2025
Directed homotopy modules
Eric Goubault
In this short note, we argue that directed homotopy can be given the structure of generalized modules, over particular monoids. This is part of a general attempt for refoundation o…