Download PDF by Hans Joachim Baues: Algebraic Homotopy

By Hans Joachim Baues

ISBN-10: 0521055318

ISBN-13: 9780521055314

Show description

Read Online or Download Algebraic Homotopy PDF

Similar topology books

Mark Andrea A De Cataldo's Hodge Theory of Projective Manifolds PDF

This booklet is a written-up and accelerated model of 8 lectures at the Hodge idea of projective manifolds. It assumes little or no history and goals at describing how the speculation turns into gradually richer and extra attractive as one specializes from Riemannian, to Kähler, to complicated projective manifolds.

Get Foundations of Symmetric Spaces of Measurable Functions: PDF

Key definitions and ends up in symmetric areas, rather Lp, Lorentz, Marcinkiewicz and Orlicz areas are emphasised during this textbook. A finished review of the Lorentz, Marcinkiewicz and Orlicz areas is gifted in keeping with suggestions and result of symmetric areas. Scientists and researchers will locate the appliance of linear operators, ergodic thought, harmonic research and mathematical physics noteworthy and worthwhile.

Additional info for Algebraic Homotopy

Example text

We now consider the category Top with the structure Top = (Top, cof, fib, I, P, 0, e). Here cof is the class of closed cofibrations in Top. 4) we see that Top satisfies (IP1) and (IP2). Strom proved that Top satisfies (IP3). 3) Proposition. Top is an IP-category. Moreover, Strom proved that Top satisfies (M2). 4) Corollary. 10). This example shows that it is convenient to consider the class cof of cofibrations as part of the structure of an 1-category. 1). 5) Proposition. Let u:C -* D be a map in C.

3) Definition. Let C be a category and let u: C -> D be a fixed map in C. We define the category C(u) = C(C -+ D) of objects under C and over D. Objects are triples (X, z, z) where u = U. x)-*(Y,y,f)isamap f:X -* Ysuchthat fz=y, yf=z. II C(u) has the initial object C C -> D and the final object C -> D -4 D. Pull backs and push outs in C(u) are given by pull backs and push outs in C. We define a natural cylinder I and a natural path space P which are functors 1, P:Top(u) -* Top(u). pp, u). We define W = P(X, x, z) by the pull back diagram in Top C w W XI pull w D where w = (u, ii).

3 Categories with a natural cylinder We here combine the notion of a cofibration category with the concept of abstract homotopy theory as introduced by Kan (1955). This concept relies on a natural cylinder object, see also Kamps. Under fairly weak assumptions on a natural cylinder we can derive the structure of a cofibration category. 1) Definition. An I-category is a category C with the structure (C, cof, 1, gyp). Here cof is a class of morphisms in C, called cofibrations. I is a functor C -> C together with natural transformations io, it and p.

Download PDF sample

Algebraic Homotopy by Hans Joachim Baues


by Daniel
4.4

Rated 4.60 of 5 – based on 16 votes