Topos

From Academic Kids

For discussion of topoi in literary theory, see literary topos. For discussion of topoi in rhetorical invention, see Inventio.

Sheaves were introduced into mathematics in the 1940s, and a major theme since then has been to study a space by studying sheaves on that space. Grothendieck expounded on this idea by introducing the notion of a topos (plural: topoi or toposes - this is a contentious topic). A topos is a type of category that behaves like the category of sheaves of sets on a topological space. The main utility of this notion is in the abundance of situations in mathematics where topological intuition is very effective but an honest topological space is lacking; it is sometimes possible to find a topos formalizing the intuition. The greatest success of this yoga to date has been the introduction of the étale topos of a scheme.


References

  • F. William Lawvere and Stephen H. Schanuel: Conceptual Mathematics: A First Introduction to Categories, Cambridge University Press, Cambridge, 1997. An "introduction to categories for computer scientists, logicians, physicists, linguists, etc." (cited from cover text).

es:Topos pl:Topos

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