Citations: Springer-Verlag - MacLane (ResearchIndex)

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MacLane S.: Homology. Classic in Math., Springer--Verlag, 1995

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Rewriting procedures generalise to Kan extensions of actions of.. - Heyworth (1999) (Correct)

....element of KB 1 . The general method of obtaining regular expressions for these computations will be given in a separate paper (see Chapter 4 of [8] 5 Applications MacLane wrote that the notion of Kan extensions subsumes all the other fundamental concepts of category theory in section 10.7 of [12] (entitled All Concepts are Kan Extensions ) So the power of rewriting theory may now be brought to bear on a much wider range of combinatorial enumeration problems. Traditionally rewriting is used for solving the word problem for monoids. It has also been used for coset enumeration problems ....

S.MacLane : \Categories for the Working Mathematician", Springer-Verlag (1971).

Representation Of Finite Groups And The First Betti Number Of.. - Toda (Correct)

....1 N 1 G N 2 1: Since any normal subgroup N of N 2 lifts to normal subgroup NN 1 of G and N 1 is maximal, N 2 N 1 is a simple group. Then validity of Schreier s conjecture (see [Gor] Theorem 1. 46) and the Eilenberg MacLane theory of the extension of 54 MASAHITO TODA groups (see e.g. [Mac] Theorem 8.8 in Chapter IX) show that G N 1 N 1 provided N 1 is non abelian. If N 1 Z p for rational prime p, it is obvious that N 2 Aut(N 1 ) Z p 1 is trivial and the lemma follows directly. Q.E.D. In view of Lemma 1 our computations in Section 6 and Section 7 turn out to be a ....

MacLane, S., Homology, Springer Verlag, 1967.

Algorithmic Computation Of De Rham Cohomology Of Complements Of.. - Walther (1999) (Correct)

....ffl [m ffl ] x1 Delta Gamma F k (A ffl [m ffl ] F k (A ffl [m ffl ] x 1 Delta F k 1 (A ffl [m ffl ] 0: By definition, the complex on the right is F k ( Omega 1 Omega A ffl [m ffl ] The mapping cone L ffl of the inclusion on the left is by Exercise II.5. 3 of [9] quasiisomorphic to the quotient on the right. However, inspecting the mapping cone definition we find that L ffl = K ffl (A ffl [m ffl ] x 1 )fkg. This proves that K ffl (A ffl [m ffl ] x 1 )fkg and F k ( Omega 1 Omega A ffl [m ffl ] are quasi isomorphic. By the inductive ....

S. MacLane. Homology. Springer-Verlag, 1991.

Lie-projective Groups - Bickel (1995) (Correct)

....and let X F be a sublimit with index category F for each subset F 2 F [fIg. Then there are, for members G F of F [ fIg, canonical arrows fGF : X F XG , such that (X I ; f F I ) is a projective limit cone over the projective system (F ; X F ; fGF ; G F ) Proof. Limits are unique by III.4 in [8]. Dualize XI.3.1 in [8] to see that a sublimit over a cofinal subset approximates the whole projective system. For the rest of the lemma we argue as follows: For a subset G let (XG ; f G i ) be a limit cone over the diagram restricted to G. Using its universal property we get the canonical ....

....with index category F for each subset F 2 F [fIg. Then there are, for members G F of F [ fIg, canonical arrows fGF : X F XG , such that (X I ; f F I ) is a projective limit cone over the projective system (F ; X F ; fGF ; G F ) Proof. Limits are unique by III.4 in [8] Dualize XI.3. 1 in [8] to see that a sublimit over a cofinal subset approximates the whole projective system. For the rest of the lemma we argue as follows: For a subset G let (XG ; f G i ) be a limit cone over the diagram restricted to G. Using its universal property we get the canonical arrow fGF for supersets F ....

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MacLane, S., ;; Kategorien," Springer--Verlag, 1972.

Cohomology For Operator Algebras: The Mayer-Vietoris Sequence - Gilfeather, Pop (Correct)

....The only non trivial verification is that is surjective, but this is the Hahn Banach extension theorem for n linear completely bounded maps into B(H) 21] for n = 1, 14] for n 2) The long exact sequence (1. 1) is then an immediate consequence of standard results in homological algebra (see [13]) We note that the maps ff n , fi n and fl n are defined as follows: ff n and fl n are induced by i and respectively, while given a completely bounded n cocycle OE on B, we extend it to a completely bounded n linear map OE on A and set fi n [OE] OE] The long exact sequence (1.2) is ....

....groups, then we say that (X 1 ; X 2 ; X ) is a cb exact triad . We note that it is not obvious whether exactness in one sense is related to exactness in the other. The first lemma is a standard result in homological algebra, which we include for the convenience of the reader. We refer to [13] for the proof. Lemma 2.1. Let C 1 fl 1 Gamma B 1 ff 1 Gamma Delta Delta Delta h 1 g 1 C 0 1 fl 1 Gamma B 0 1 ff 0 1 Gamma Delta Delta Delta Delta Delta Delta Gamma A n fi n Gamma C n 1 fl n 1 Gamma B n 1 ff n 1 Gamma A n 1 Gamma Delta Delta ....

S. MacLane, Homology, Springer Verlag, Berlin, 1995.

Singular Homology of Abstract Algebraic Varieties. - Suslin, Voevodsky (1996) (17 citations) (Correct)

....the embeddings i 0 ; i 1 : X Gamma X Theta A 1 defined by the points 0; 1 of A 1 . The induced homomorphisms of complexes i 0 ; i 1 : F(X Theta A 1 Theta Delta : Gamma F(X Theta Delta : are homotopic. Proof: One can use the usual topological homotopy operator (see [14][ch.2,x8] Define a homomorphism s p : F(X Theta A 1 Theta Delta p ) Gamma F(X Theta Delta p 1 ) by the formula s p = p X i=0 ( Gamma1) i (Id X Theta i ) where i : Delta p 1 Gamma Delta p Theta A 1 is the linear isomorphism taking v j to v j Theta 0 if j ....

S. MacLane. Homology. Springer-Verlag, 1963.

Simplicial Perturbation Techniques and Eective Homology - Rocio Gonzalez-Daz Belen Self-citation (Homology) (Correct)

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MacLane S.: Homology. Classic in Math., Springer--Verlag, 1995

Reusing Integer Homology Information of - Binary Digital Images Self-citation (Homology) (Correct)

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MacLane S.: Homology. Classic in Math., Springer--Verlag, 1995

Algorithms In Algebraic Topology And Homological.. - Hurado, Alvarez.. Self-citation (Maclane) (Correct)

....the complexity of computing the Steenrod squares of cochains. 2. Preliminaries Although relevant notions of homological algebra are explained through the exposition of this survey, most of the common concepts are not explicitly given and are used without further explanations (for details, see [10, 28]) We recall the notions of DG module and DG algebra. DG modules and DG algebras. Our ground ring # is Z or Z localized at a prime p.A di#erential graded module (M,d) is a module M graded on the positive integers and endowed with a di#erential operator d of degree such that d#d = 0. The ....

S. MacLane, Homology, Springer-Verlag, Berlin (1995).

Homology, Homotopy and Applications, vol.?(?), 2004, pp.1--14 - Hpt And Cocyclic (Correct)

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S. McLane. Homology. Classics in Math., Springer--Verlag, Berlin, 1995.

Computing Adem Cohomology Operations - Rocio Gonzalez--Diaz Pedro (Correct)

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S. MacLane. Homology. Classics in Math., Springer--Verlag,

Torus Actions, Equivariant Moment-Angle - Complexes And Coordinate (Correct)

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S. Maclane, Homology, Springer-Verlag, Berlin, 1963.

Torus Actions, Combinatorial Topology And - Homological Algebra Victor (Correct)

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S. Maclane, Homology, Springer-Verlag, Berlin, 1963.

A Unified View on Filter Banks - Klappenecker, Holschneider (2000) (Correct)

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S. MacLane, Homology, Springer Verlag, Berlin, 1963.

Notes on the Reidemeister Torsion - Nicolaescu (2002) (Correct)

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S. MacLane: Homology, Band 114, Springer-Verlag 1963.