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functorial morphism

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  • Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… …   Wikipedia

  • Homological algebra — is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract… …   Wikipedia

  • Vector bundle — The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… …   Wikipedia

  • Universal property — In various branches of mathematics, certain constructions are frequently defined or characterised by an abstract property which requires the existence of a unique morphism under certain conditions. These properties are called universal properties …   Wikipedia

  • Limit (category theory) — In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint… …   Wikipedia

  • Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

  • Functor — For functors as a synonym of function objects in computer programming to pass function pointers along with its state, see function object. For the use of the functor morphism presented here in functional programming see also the fmap function of… …   Wikipedia

  • Enriched category — In category theory and its applications to mathematics, an enriched category is a category whose hom sets are replaced by objects from some other category, in a well behaved manner.DefinitionWe define here what it means for C to be an enriched… …   Wikipedia

  • Factorization system — In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in category theory.DefinitionA… …   Wikipedia

  • Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… …   Wikipedia

  • Grothendieck–Hirzebruch–Riemann–Roch theorem — In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a… …   Wikipedia

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