The Brown-Golasinski model structure on strict -groupoids revisited

نویسندگان

  • Dimitri Ara
  • François Métayer
چکیده

We prove that the folk model structure on strict ∞-categories transfers to the category of strict ∞-groupoids (and more generally to the category of strict (∞, n)categories), and that the resulting model structure on strict ∞-groupoids coincides with the one defined by Brown and Golasiński via crossed complexes.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Orbifolds as a Localization of the 2-category of Groupoids

Abstract. We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call “covers,” then the strict 2-category structure drops down to the localization. In our construction the spaces of 1and 2-arrows admit natural topologies, the space of morphisms (1-arro...

متن کامل

Homotopy types of strict 3-groupoids

It has been difficult to see precisely the role played by strict n-categories in the nascent theory of n-categories, particularly as related to n-truncated homotopy types of spaces. We propose to show in a fairly general setting that one cannot obtain all 3-types by any reasonable realization functor 1 from strict 3-groupoids (i.e. groupoids in the sense of [20]). More precisely we show that on...

متن کامل

Covering Groups of Non-connected Topological Groups Revisited

All spaces are assumed to be locally path connected and semi-locally 1-connected. Let X be a connected topological group with identity e, and let p : X̃ → X be the universal cover of the underlying space of X. It follows easily from classical properties of lifting maps to covering spaces that for any point ẽ in X̃ with pẽ = e there is a unique structure of topological group on X̃ such that ẽ is th...

متن کامل

The Strict ω-Groupoid Interpretation of Type Theory

Hofmann and Streicher showed that there is a model of the intensional form of Martin-Löf’s type theory obtained by interpreting closed types as groupoids. We show that there is also a model when closed types are interpreted as strict ω-groupoids. The nonderivability of various truncation and uniqueness principles in intensional type theory is then an immediate consequence. In the process of con...

متن کامل

On Prime and Semiprime Ideals in Ordered AG-Groupoids

The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017