Abstract: We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like $\mathrm{Ext}$ and $\mathrm{Tor}$ over a commutative coherent ring $R$? We give an answer by introducing category constructors that enable us to build up a category which is both suited for performing explicit calculations and equivalent to the category of all finitely presented functors. The second question is: how do we determine the differentials on the pages of a spectral sequence associated to a filtered cochain complex only in terms of operations directly provided by the axioms of an abelian category? Its answer relies on a constructive method for performing diagram chases based on a calculus of relations within an arbitrary abelian category.
Publication Year: 2019
Publication Date: 2019-08-12
Language: en
Type: preprint
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Cited By Count: 2
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