Webis that the class of geometric lattices, which is cryptomorphic to the category of simple matroids, is the same as the class of intersection lattices of arrangements of homotopy spheres. The interpretation of a geometric lattice as an arrangement of ho-motopy spheres is a natural generalization of the Folkman-Lawrence theorem. WebCryptomorphism In mathematics, two objects, especially systems of axioms or semantics for them, are called cryptomorphic if they are equivalent but not obviously equivalent. This word is a play on the many morphisms in mathematics, but "cryptomorphism" is only very distantly related to "isomorphism", "homomorphism", or "morphisms".
cryptomorphic - Wiktionary
Web( mathematics) Two objects, especially systems of axioms or semantics for them, are called cryptomorphic if they are equivalent (possibly in some informal sense) but not obviously … WebWhile this variety of axiom systems (that is to say the number of cryptomorphic definitions a matroid) gives matroid theory much of its power, it can often contribute to the difficulty in learning the subject. We suggest the reader keep the prototypes in mind while learning the formal definitions and refer often to the cryptomorphism charts. detached garage and pool house
Two cryptomorphic formalizations of projective incidence …
In mathematics, two objects, especially systems of axioms or semantics for them, are called cryptomorphic if they are equivalent but not obviously equivalent. In particular, two definitions or axiomatizations of the same object are "cryptomorphic" if it is not obvious that they define the same object. Examples of … See more The word was coined by Garrett Birkhoff before 1967, for use in the third edition of his book Lattice Theory. Birkhoff did not give it a formal definition, though others working in the field have made some attempts since. See more Its informal sense was popularized (and greatly expanded in scope) by Gian-Carlo Rota in the context of matroid theory: there are dozens of equivalent axiomatic approaches to … See more • Combinatorial class, an equivalence among combinatorial enumeration problems hinting at the existence of a cryptomorphism See more WebAs a noun object is a thing that has physical existence. As a verb object is to disagree with something or someone; especially in a court of law, to raise an objection. As an adjective … detached garage ceiling insulation