Facebook Twitter Google Share on Facebook homotopy (redirected fromHomotopy invariance) homotopy [hō′mäd·ə·pē] (mathematics) Between two mappings of the same topological spaces, a continuous function representing how, in a step-by-step fashion, the image of one mapping can be continuousl...
In the case of commutative Gorenstein rings we prove that up to a natural isomorphism our equivalence extends Iyengar鈥揔rause's equivalence.doi:10.1016/j.jalgebra.2010.09.002Xiao-Wu ChenElsevier Inc.Journal of AlgebraXiao-Wu Chen, Homotopy equivalences induced by balanced pairs, Journal of Algebra...
Twitter Google Share on Facebook homotopy (redirected fromHomotopy class) homotopy [hō′mäd·ə·pē] (mathematics) Between two mappings of the same topological spaces, a continuous function representing how, in a step-by-step fashion, the image of one mapping can be continuously deformed on...
We give sufficient conditions under which the balanced pair of subcategories gives rise to equivalent homotopy categories of complexes. As an application, we prove that for a left-Gorenstein ring, there exists a triangle-equivalence between the homotopy category of its Gorenstein projective modules and...
As for classical A∞ , L∞ , etc cases, these theorems imply that OCHA–quasi-isomorphisms and in particular the one in Theorem 3.2 in fact give homotopy equivalence between OCHAs. This further implies the uniqueness of a minimal model for an OCHA (H, l, n); a minimal OCHA H(H) ...
In traditional mathematics that would be blatantly wrong — there are many isomorphic objects that are not equal. But with the HoTT’s notion of equality, there is nothing that would contradict it. In fact, the statement thatequivalence is equivalent to equalitycan be added to HoTT as an axio...
Two such combinatorial q-loops of simplices are A-homotopic if they can be deformed into each other without breaking any q-dimensional connections. More precisely, we have the following definition. Definition 1.2 Let ≃A be the equivalence relation on the collection of q-loops in Δ, based...
(Bloomington, April 1st). Throughout Top will denote a category of “nice” spaces, say, compactly generated Hausdorff spaces or simply CW-complexes. We shall start with two preliminary definitions: Definition 1. A map f : X // Y is a weak homotopy equivalence, if the induced ...
theoryinthiscategory.Theequivalenceofthesecategoriesunderadjointfunctors(see[14],[6],[5],[4])playedanimportantroleinthedevelopmentofgeometrictopology.Inthelate60's,Quillen[16]usedthenotionofclassifyingspaceforasmallcategory[17],andshowedtheimportanceofdoinghomotopytheoryinthecategoryofsmallcategories.Latch[8...
By a result of Kedra and Pinsonnault, we know that the topology of groups of symplectomorphisms of symplectic 4-manifolds is complicated in general. Howeve