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# Relative Homotopy in Relational Structures

Published:2008-06-01
Printed: Jun 2008
• P. J. Witbooi
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## Abstract

The homotopy groups of a finite partially ordered set (poset) can be described entirely in the context of posets, as shown in a paper by B. Larose and C. Tardif. In this paper we describe the relative version of such a homotopy theory, for pairs $(X,A)$ where $X$ is a poset and $A$ is a subposet of $X$. We also prove some theorems on the relevant version of the notion of weak homotopy equivalences for maps of pairs of such objects. We work in the category of reflexive binary relational structures which contains the posets as in the work of Larose and Tardif.
 Keywords: binary reflexive relational structure, relative homotopy group, exact sequence, locally finite space, weak homotopy equivalence
 MSC Classifications: 55Q05 - Homotopy groups, general; sets of homotopy classes 54A05; - unknown classification 54A05;18B30 - Categories of topological spaces and continuous mappings [See also 54-XX]