Effective Homology of the Pushout of Simplicial Sets

TL;DR

This paper presents an algorithm to compute the effective homology of the pushout of simplicial sets with effective homology, enabling practical calculations in algebraic topology.

Contribution

It introduces a novel algorithm for constructing the effective homology of pushouts of simplicial sets, extending computational tools in algebraic topology.

Findings

Algorithm successfully computes effective homology of pushouts

Enables practical calculations in algebraic topology

Extends existing computational methods for simplicial sets

Abstract

In this paper, an algorithm building the effective homology version of the pushout of the simplicial morphisms $f:X\rightarrow Y$ and $g:X\rightarrow Z$, where $X,Y$ and $Z$ are simplicial sets with effective homology is presented.