منابع مشابه
Algebraic Properties of Homotopies
The scheme ExFunc3CondD deals with a non empty set A, three unary functors F , G, and H yielding sets, and three unary predicates P, Q, R, and states that: There exists a function f such that dom f = A and for every element c of A holds if P[c], then f(c) = F(c) and if Q[c], then f(c) = G(c) and if R[c], then f(c) = H(c) provided the parameters meet the following conditions: • For every element...
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We present a new algorithmic framework which utilizes tropical geometry and homotopy continuation for solving systems of polynomial equations where some of the polynomials are generic elements in linear subspaces of the polynomial ring. This approach generalizes the polyhedral homotopies by Huber and Sturmfels.
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We exhibit a model structure on 2-Cat, obtained by transfer from sSet across the adjunction C2 ◦ Sd a Ex ◦ N2. A certain class of homotopies in this model structure turns out to be in 1-to-1 correspondence with strong simulations among labeled transitions systems, formalising the geometric intuition of simulations as deformations. The correspondence still holds in the cubical setting, character...
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We show “free theorems” in the style of Wadler on homotopy type theory as consequences of relational parametricity. It follows that, for each space, its higher inductive definition and impredicative definition have the same homotopy groups. An impredicative definition of a space can help us to find generators of homotopy groups of the space.
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As is pointed out in [Smith (1997)], in many applications of quasigroups isotopies and homotopies are more important than isomorphisms and homomorphisms. In this paper, the way homotopies may arise in the context of categorical quasigroup model theory is investigated. In this context, the algebraic structures are specified by diagram-based logics, such as sketches, and categories of models beco...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1968
ISSN: 0019-2082
DOI: 10.1215/ijm/1256054315