Homotopy Theory of Modules
Absolute and Relative Homotopy Groups of Modules using the Injective Homotopy Category
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Homological algebra generalizes the construction of
(co-)homology theory of topological spaces, making it
available for algebraic theories. In a similar vein,
the homotopy theory of modules attempts to imitate
topological homotopy theory. A discussion of the
categorical notion of duality precedes the definition
of the injective homotopy category. The absolute and
relative homotopy groups are then defined and
investigated. Finally, the homotopy groups of the
cyclic group C_m are calculated for trivial C_m-modules.
(co-)homology theory of topological spaces, making it
available for algebraic theories. In a similar vein,
the homotopy theory of modules attempts to imitate
topological homotopy theory. A discussion of the
categorical notion of duality precedes the definition
of the injective homotopy category. The absolute and
relative homotopy groups are then defined and
investigated. Finally, the homotopy groups of the
cyclic group C_m are calculated for trivial C_m-modules.
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