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Linearization of algebraic structures via functor calculus

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Abstract

As the result of a long optimization process in categorical algebra, the notion of semi-abelian category allows for developing highly non-trivial algebraic theory in a very general framework which encompasses almost all algebraic structures usually studied, and even certain types of objects having additional topological or analytic structures, such as compact topological groups and C$^*$-algebras. In particular, a new approach to commutator theory, internal object actions including the important special case of representations (Beck modules), to crossed modules and cohomology is being developed in this framework. This even leads to the foundation of categorical Lie theory generalizing both classical Lie theory (for groups) and recent non-associative Lie theory (for loops) to a broad variety of other non-linear algebraic structures. The key new tool consists of an (algebraic) functor calculus in the framework of semi-abelian categories.
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Dates and versions

hal-03177629 , version 1 (23-03-2021)

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  • HAL Id : hal-03177629 , version 1

Cite

Manfred Hartl. Linearization of algebraic structures via functor calculus. International Conference on Combinatorial and Toric Homotopy, Aug 2015, Singapore, Singapore. ⟨hal-03177629⟩
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