منابع مشابه
Adjoint Functors and Heteromorphisms
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades, the notion of adjoint functors has moved to centerstage as category theory’s primary tool to characterize what is important in mathematics. Our focus here i...
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A family T of digraphs is a complete set of obstructions for a digraph H if for an arbitrary digraph G the existence of a homomorphism from G to H is equivalent to the non-existence of a homomorphism from any member of T to G. A digraph H is said to have tree duality if there exists a complete set of obstructions T consisting of orientations of trees. We show that if H has tree duality, then it...
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There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms (object-to-object morphisms between objects of different categories) that parses an adjunction into two separate parts (left and right representations of heterom...
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We study co-Frobenius and more generally quasi-co-Frobenius corings over arbitrary base rings and over PF base rings in particular. We generalize some results about co-Frobenius and quasi-co-Frobenius coalgebras to the case of noncommutative base rings and give several new characterizations for co-Frobenius and more generally quasi-co-Frobenius corings, some of them are new even in the coalgebr...
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We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors F : A → MA from a pointed category with coproducts to A-modules in terms of differentials of F . Here A is a commutative S-algebra. We specialize to the case when A is the category of a-algebras for an operad a and F is the forgetful functor, and derive mild...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1965
ISSN: 0019-2082
DOI: 10.1215/ijm/1256068141