By Kamps K.H., Porter T.
Read Online or Download 2-Groupoid Enrichments in Homotopy Theory and Algebra PDF
Similar algebra books
The second one quantity keeps the process learn all started in quantity 1, yet can be utilized independently by means of these already owning an undemanding wisdom of the topic. A precis of easy team conception is via bills of staff homomorphisms, jewelry, fields and crucial domain names. The comparable recommendations of an invariant subgroup and an amazing in a hoop are introduced in and the reader brought to vector areas and Boolean algebra.
- Communications in Algebra, volume 26, number 1, 1998
- The W₃ algebra: modules, semi-infinite cohomology, and BV algebras
- Integral moments (2008)(en)(17s)
- Group Psychotherapy for Women With Breast Cancer
Extra resources for 2-Groupoid Enrichments in Homotopy Theory and Algebra
KAMPS AND T. PORTER Appendix For convenience we include here a sketch of Crans description of Gray categories as algebraic structures (cf. [Cr]), but for convenience have inverted the interchange 3-cell, adjusting throughout. A Gray category C consists of collections C0 of objects, C1 of arrows, C2 of 2-arrows and C3 of 3-arrows together with • functions sn , tn : Ci −→ Cn for all 0 n < i 3 called n-source and n-target, • functions n : Cn+1 sn ×tn Cn+1 −→ Cn+1 for all 0 n < 3 called vertical composition, • functions n : Ci sn ×tn Cn+1 −→ Ci and n : Cn+1 sn ×tn Ci −→ Ci for all 0 n 1, n + 1 < i 3, called whiskering, • a function 0 : C2 s0 ×t0 C2 −→ C3 , called horizontal composition, and • functions id− : Ci −→ Ci+1 for all 0 i 2, called identity, such that (i) C is a globular set, (ii) for every C, C ∈ C0 , the collection of elements of C with 0-source C and 0-target C forms a 2-category C(C, C ) with n-composition in C(C, C ) given by n+1 and identities given by id− , (iii) for every g : C −→ C in C1 and every C and C in C0 , − 0 g is a 2-functor, C(C , C ) −→ C(C , C ) and g 0 − is a 2-functor C(C, C ) −→ C(C, C ), (iv) for every C in C0 and every C, C in C0 , − 0 idC , is equal to the identity functor on C(C , C ) and idC 0 − is equal to the identity functor on C(C, C ), (v) for every γ , δ ∈ C2 with t0 (γ ) = s0 (δ), γ : f ⇒ f and δ : g ⇒ g , s2 (δ t2 (δ 0 0 γ ) = (δ γ ) = (g f) 0 γ) 0 1 1 (g (δ 0 0 γ ), f) and δ 0 γ is an iso − 3-arrow, (It may help to draw the diagrams to identify what this axiom states.
And Kelly, G. : Closed categories, In: Proc. Conference on Categorical Algebra, (La Jolla, 1965), Springer, New York, 1966, pp. 421–562. Ellis, G. J. : Higher dimensional crossed modules and the homotopy groups of (n + 1)-ads, J. Pure Appl. Algebra 46 (1987), 117–136. Fantham, P. H. H. : Groupoid enriched categories and homotopy theory, Canad. J. Math. 35 (1983), 385–416. Gabriel, P. : Calculus of Fractions and Homotopy Theory, Ergeb. Math. Grenzgeb. 35, Springer, New York, 1967. : Categorically algebraic foundations for homotopical algebra, Appl.
Monoidal globular categories as a natural environment for the theory of weak n-categories, Adv. Math. 136 (1998), 39–103. : Double loop spaces, braided monoidal categories and algebraic 3-type of space, Preprint, Nice, 1997. : M´ethode n-cat´egorique d’interpr´etation des complexes et des extensions abeliennes de longueur n, Preprint, Inst. Math. Louvain-la-Neuve, Rapport no 45 (1982). : Produits tensoriels coh´erents de complexes de chaˆıne, Bull. Soc. Math. Belg. 41 (1989), 219–247. , Hardie, K.
2-Groupoid Enrichments in Homotopy Theory and Algebra by Kamps K.H., Porter T.