In 1971, Bott gave a some talks in Mexico at the IPN, in a conference on differential topology sponsored by UNAM, on his work on obstructions to integrability of foliations. These talks were published Ithink in an LNM volume 279. He also described a general construction of a simplicial complex BC associating a simplex to each commutative diagram of a certain shape in a category C. While he attributed this general construction perhaps to Grothendieck, as I recall he said it went back to work of Segal.
According to a paper of Madsen and Weiss mentioned in the nice link provided by David Roberts, this construction has some relation to the moduli space of Riemann surfaces, perhaps the first example of associating a topological space to a category. Namely, if G is the group of isotopy classes of automorphisms of a surface of suitably high genus, then BG has the same rational cohomology as the moduli space of stable Riemann surfaces.
In1971,BottgaveasometalksinMexicoat the conceptIPN,inaconferenceondifferentialtopologysponsoredbyUNAM,onhisworkonobstructionstointegrabilityoffoliations.ThesetalkswerepublishedIthinkinanLNMvolume.Healsodescribedageneralconstruction of asimplicialcomplexBCassociatingasimplextoeachcommutativediagramofacertainshapeinacategoryC.WhileheattributedthisgeneralconstructionperhapstoGrothendieck,asIrecallhesaiditwentbacktoworkofSegal.
AccordingtoapaperofMadsenandWeissmentionedin the nicelinkprovidedbyDavidRoberts,thisconstructionhassomerelationtothe moduli space of "Riemann surfaces'as,perhaps the first example ofassociatingatopologicalspacetoacategory. ButmaybeIwasborntoosoonNamely,ifGisthegroupofisotopyclassesofautomorphismsofasurfaceofsuitablyhighgenus,thenBGhasthesamerationalcohomologyasthemodulispaceofstableRiemannsurfaces.