We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. It was already shown in [1] that the inclusion of the first space into the second one is a homotopy equivalence. In this paper we prove that the homotopy types of the terms of the natural ‘degree’ filtration approximate closer and closer the homotopy type of the space o...

This paper proves that the functor C(∗) that sends pointed, simply-connected CW-complexes to their chain-complexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type — even inducing an equivalence of categories between the category of CW-complexes up to homotopy equivalence and a certain category of chain-complexes equipped with higher diagonals. Cons...

2 Homotopy λ-calculus 16 1 Type systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Homotopy λ-calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Basic layer syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4 Basic layer semantics in Top . . . . . . . . . . . . . . . . . . . . . . . . ...

We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability. The main result, which was known for simplicially-enriched categories, links homotopy locally presentable V-categories with combinatorial model V-categories, in the case where all objects of V are cofibrant.

This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new definition of T-homotopy equivalence is proposed, following the intuition of refinement of obser...

Homotopy And Simple Homotopy Theory Find loads of the abstract homotopy and simple homotopy theory book catalogues in this site as the choice of you visiting this page. You can also join to the website book library that will show you numerous books from any types. Literature, science, politics, and many more catalogues are presented to offer you the best book to find. The book that really makes...

We present a definition of homotopy algebra for an operad, and explore its consequences. The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After a review of operads and monoidal categories, the definition of homotopy algebra is given. Specifically, suppose that M is a monoidal category in which it makes sense to talk about algebras for some o...

Homotopy And Simple Homotopy Theory We may not be able to make you love reading, but abstract homotopy and simple homotopy theory will lead you to love reading starting from now. Book is the window to open the new world. The world that you want is in the better stage and level. World will always guide you to even the prestige stage of the life. You know, this is some of how reading will give yo...

The goal of this paper is to study the homotopy theory of homotopy algebras over a Koszul operad with their infinity morphisms. The method consists in endowing the category of coalgebras over the Koszul dual cooperad with a model category structure. CONTENTS Introduction 1 1. Recollections 2 2. Model category structure for coalgebras 5 3. Conclusion 14 Appendix A. A technical lemma 15 Reference...