Topological properties
... 2.1. Definition and first examples. Probably many of you have seen the notion of compact space in the context of subsets of Rn , as sets which are closed and bounded. Although not obviously at all, this is a topological property (it can be defined using open sets only). Definition 4.14. Given a topo ...
... 2.1. Definition and first examples. Probably many of you have seen the notion of compact space in the context of subsets of Rn , as sets which are closed and bounded. Although not obviously at all, this is a topological property (it can be defined using open sets only). Definition 4.14. Given a topo ...
![arXiv:1510.01797v3 [math.CT] 21 Apr 2016 - Mathematik, Uni](http://s1.studyres.com/store/data/003897650_1-5601c13b5f003f1ac843965b9f00c683-300x300.png)
Algebraic models for rational G
... where Σ∞ X denotes the suspension spectrum on X and square brackets denote homotopy classes of maps. Therefore we might study cohomology theories by studying the corresponding spectra. What is more, on the level of spectra the information we are interested in is up to homotopy, that is we want to wo ...
... where Σ∞ X denotes the suspension spectrum on X and square brackets denote homotopy classes of maps. Therefore we might study cohomology theories by studying the corresponding spectra. What is more, on the level of spectra the information we are interested in is up to homotopy, that is we want to wo ...
![arXiv:math/0009100v1 [math.DG] 10 Sep 2000](http://s1.studyres.com/store/data/000152175_1-8b3fe2b443d17ea217220901b35aa35c-300x300.png)
Derived algebraic geometry
... of which have the equation x = 0. In this case, the affine ring of the scheme theoretic intersection is given by C[x, y]/(x, x) ' C[y]. This ring has dimension one, rather than the expected dimension zero, because the two equations are not independent: setting x = 0 twice is equivalent to setting x ...
... of which have the equation x = 0. In this case, the affine ring of the scheme theoretic intersection is given by C[x, y]/(x, x) ' C[y]. This ring has dimension one, rather than the expected dimension zero, because the two equations are not independent: setting x = 0 twice is equivalent to setting x ...
Lecture notes of Dr. Hicham Gebran
... Remark 1.5 A set which is not open is not necessarily closed. For example ]0,1] is neither open nor closed. Also a set can be both open and closed. Indeed, in any metric space X, ∅ and X are closed an open. Here is another example. Let d be the discrete distance on a set X containing more than one p ...
... Remark 1.5 A set which is not open is not necessarily closed. For example ]0,1] is neither open nor closed. Also a set can be both open and closed. Indeed, in any metric space X, ∅ and X are closed an open. Here is another example. Let d be the discrete distance on a set X containing more than one p ...
Contents 1. Introduction 2 2. The monoidal background 5 2.1
... Our main result, theorem 4.3.1, is an acyclic models theorem for monoidal functors from a monoidal category C to the monoidal category C∗ (Z). We likewise establish several variations of this result, which cover the symmetric monoidal and the contravariant monoidal settings. As a consequence of our ...
... Our main result, theorem 4.3.1, is an acyclic models theorem for monoidal functors from a monoidal category C to the monoidal category C∗ (Z). We likewise establish several variations of this result, which cover the symmetric monoidal and the contravariant monoidal settings. As a consequence of our ...
Factorization homology of stratified spaces
... Remark 0.4. In this work, we use Joyal’s quasi-category model of ∞-category theory [Jo]. Boardman & Vogt first introduced these simplicial sets in [BV], as weak Kan complexes, and their and Joyal’s theory has been developed in great depth by Lurie in [Lu1] and [Lu2], our primary references; see the ...
... Remark 0.4. In this work, we use Joyal’s quasi-category model of ∞-category theory [Jo]. Boardman & Vogt first introduced these simplicial sets in [BV], as weak Kan complexes, and their and Joyal’s theory has been developed in great depth by Lurie in [Lu1] and [Lu2], our primary references; see the ...
Topological vector spaces
... or C × V into V , as appropriate. This uses the product topology on R × V or C × V associated to the standard topology on R or C and the given topology on V . Some authors include the additional condition that {0} be a closed set in V , and we shall follow this convention here as well. Note that a t ...
... or C × V into V , as appropriate. This uses the product topology on R × V or C × V associated to the standard topology on R or C and the given topology on V . Some authors include the additional condition that {0} be a closed set in V , and we shall follow this convention here as well. Note that a t ...
Galois actions on homotopy groups of algebraic varieties
... as Galois representations, by recovering them from cohomology groups of smooth Weil sheaves, thereby extending the author’s paper [38] from fundamental groups to higher homotopy groups, and indeed to the whole homotopy type. Corollaries 7.4 and 7.36 give similar results for `–adic and p –adic homoto ...
... as Galois representations, by recovering them from cohomology groups of smooth Weil sheaves, thereby extending the author’s paper [38] from fundamental groups to higher homotopy groups, and indeed to the whole homotopy type. Corollaries 7.4 and 7.36 give similar results for `–adic and p –adic homoto ...
TRACES IN SYMMETRIC MONOIDAL CATEGORIES Contents
... Every object of nCob is dualizable: the evaluation and coevaluation are both M ×[0, 1], regarded either as a cobordism from ∅ to M tM or from M tM to ∅. The trace of a cobordism from M to M is the closed n-manifold obtained by gluing the two components of its boundary together. In particular, the Eu ...
... Every object of nCob is dualizable: the evaluation and coevaluation are both M ×[0, 1], regarded either as a cobordism from ∅ to M tM or from M tM to ∅. The trace of a cobordism from M to M is the closed n-manifold obtained by gluing the two components of its boundary together. In particular, the Eu ...
