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...

We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary homotopy for functors. The 1-homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the notion of orbifold 1-homotopy type induced by a 1-homotopy between presentations of the orbif...

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...

Certain naturally occurring spaces have isomorphic v1-periodic homotopy groups. To each is associated a mapping telescope whose ordinary homotopy groups equal the v1-periodic homotopy groups of the space. It is proved that the mapping telescopes of the spaces are homotopy equivalent.