scholarly journals Recognition principle for generalized Eilenberg-Mac Lane spaces

2001 ◽  
pp. 21-26 ◽  
Author(s):  
Bernard Badzioch
Keyword(s):  
Mac Lane

scholarly journals The strength of Mac Lane set theory

2001 ◽  
Vol 110 (1-3) ◽  
pp. 107-234 ◽  
Author(s):  
A.R.D. Mathias
Keyword(s):  
Set Theory ◽  
Mac Lane

scholarly journals Braided premonoidal Mac Lane coherence

2004 ◽  
Vol 190 (1-3) ◽  
pp. 155-176 ◽  
Author(s):  
William P. Joyce
Keyword(s):  
Mac Lane

scholarly journals Proof of a Conjecture of S. Mac Lane

1996 ◽  
Vol 3 (61) ◽  
Author(s):  
Sergei Soloviev
Keyword(s):  
Linear Logic ◽  
Sufficient Conditions ◽  
Vector Spaces ◽  
Categorical Equivalence ◽  
Closed Category ◽  
Symmetric Monoidal Closed Category ◽  
Monoidal Closed Category ◽  
Coherence Theorem ◽  
Mac Lane

Some sufficient conditions on a Symmetric Monoidal Closed category K are obtained such that a diagram in a free SMC category generated by the set A of atoms commutes if and only if all its interpretations in K are commutative. In particular, the category of vector spaces on any field satisfies these conditions (only this case was considered in the original Mac Lane conjecture). Instead of diagrams, pairs of derivations in Intuitionistic Multiplicative Linear logic can be considered (together with categorical equivalence). Two derivations of the same sequent are equivalent if and only if all their interpretations in K are equal. In fact, the assignment of values (objects of K) to atoms is defined constructively for each pair of derivations. Taking into account a mistake in R. Voreadou's proof of the "abstract coherence theorem" found by the author, it was necessary to modify her description of the class of non-commutative diagrams in SMC categories; our proof of S. Mac Lane conjecture proves also the correctness of the modified description.

scholarly journals SUR LES GROUPES D'EILENBERG-MAC LANE. II

1954 ◽  
Vol 40 (8) ◽  
pp. 704-707 ◽  
Author(s):  
H. Cartan
Keyword(s):  
Mac Lane

Symmetric Powers of Motives

2019 ◽  
pp. 232-252
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Topological Space ◽  
Symmetric Group ◽  
Homotopy Group ◽  
Orbit Space ◽  
Symmetric Power ◽  
Homotopy Groups ◽  
Integral Homology ◽  
Symmetric Powers ◽  
Mac Lane ◽  
Abelian Monoid

This chapter develops the basic theory of symmetric powers of smooth varieties. The constructions in this chapter are based on an analogy with the corresponding symmetric power constructions in topology. If 𝐾 is a set (or even a topological space) then the symmetric power 𝑆𝑚𝐾 is defined to be the orbit space 𝐾𝑚/Σ‎𝑚, where Σ‎𝑚 is the symmetric group. If 𝐾 is pointed, there is an inclusion 𝑆𝑚𝐾 ⊂ 𝑆𝑚+1𝐾 and 𝑆∞𝐾 = ∪𝑆𝑚𝐾 is the free abelian monoid on 𝐾 − {*}. When 𝐾 is a connected topological space, the Dold–Thom theorem says that ̃𝐻*(𝐾, ℤ) agrees with the homotopy groups π‎ *(𝑆∞𝐾). In particular, the spaces 𝑆∞(𝑆 𝑛) have only one homotopy group (𝑛 ≥ 1) and hence are the Eilenberg–Mac Lane spaces 𝐾(ℤ, 𝑛) which classify integral homology.

scholarly journals Spectral Sequence for Mac Lane Homology

1994 ◽  
Vol 170 (2) ◽  
pp. 422-428 ◽  
Author(s):  
T. Pirashvili
Keyword(s):  
Spectral Sequence ◽  
Mac Lane
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