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# biogroupoids: mathematical models of species evolution

# 0.1 Introduction

*Biogroupoids*, $\mathcal{G_{B}}$, were introduced as mathematical representations of
evolving biological species ([1, 2]) generated by *weakly equivalent classes of living organisms*, $E_{O}$, specified by inter-breeding organisms;in this case, a *weak equivalence relation*, $\sim_{w}$, is defined on the set of evolving organisms modeled in terms of functional, *isomorphic genome networks*, $G_{{iso}}^{N}$, such as those described by $LM_{n}$-logic networks in Łukasiewicz-Moisil, ${\mathcal{L}M}_{n}$ topoi ([1]).

# 0.2 AT-Formulation

This concept allows an algebraic topology formulation of the origin of species and biological evolution both at organismal/organismic and biomolecular levels; it represents a new approach to biological evolution from the standpoint of super-complex systems biology.

# References

- 1
Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks.,
*Axiomathes*, 16 Nos. 1-2: 65-122. - 2 Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007, Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness, Axiomathes, 17: 35-168.

## Mathematics Subject Classification

00A05*no label found*92B05

*no label found*03G20

*no label found*92D15

*no label found*

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