(monomorphism)
31Image (category theory) — Given a category C and a morphism f:X ightarrow Y in C , the image of f is a monomorphism h:I ightarrow Y satisfying the following universal property: #There exists a morphism g:X ightarrow I such that f = hg . #For any object Z with a morphism k …
32Local quantum field theory — The Haag Kastler axiomatic framework for quantum field theory, named after Rudolf Haag and Daniel Kastler, is an application to local quantum physics of C* algebra theory. It is therefore also known as Algebraic Quantum Field Theory (AQFT). The… …
33Equivalence of categories — In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are essentially the same . There are numerous examples of categorical equivalences… …
34Category of topological spaces — In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again… …
35Subobject — In category theory, there is a general definition of subobject extending the idea of subset and subgroup.In detail, suppose we are given some category C and monomorphisms: u : S rarr; A and: v : T rarr; A . We say u factors through v and write :… …
36Category of groups — In mathematics, the category Grp has the class of all groups for objects and group homomorphisms for morphisms. As such, it is a concrete category. The study of this category is known as group theory.The monomorphisms in Grp are precisely the… …
37Glossary of category theory — This is a glossary of properties and concepts in category theory in mathematics.CategoriesA category A is said to be: * small provided that the class of all morphisms is a set (i.e., not a proper class); otherwise large. * locally small provided… …
38Hall's universal group — In algebra, Hall s universal group isa countable locally finite group, say U , which is uniquely characterized by the following properties.* Every finite group G admits a monomorphism to U .* All such monomorphisms are conjugate by inner… …
39Section (category theory) — In category theory, a branch of mathematics, a section (or coretraction) is a right inverse of a morphism. Dually, a retraction (or retract) is a left inverse. In other words, if and are morphisms whose composition is the identity morphism on Y,… …
40A¹ homotopy theory — In algebraic geometry and algebraic topology, a branch of mathematics, A1 homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to… …
