اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInvolutive Weak Globular Higher Categories
93
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate the notion of involutive weak globular $omega$-categories via Jacque Penons approach. In particular, we give the constructions of a free self-dual globular $omega$-magma, of a free strict involutive globular $omega$-category, over an $omega$-globular set, and a contraction between them. The monadic definition of involutive weak globular $omega$-categories is given as usual via algebras for the monad induced by a certain adjunction. In our case, the adjunction is obtained from the free functor that associates to every $omega$-globular set the above contraction. Some examples of involutive weak globular $omega$-categories are also provided.
قيم البحث
اقرأ أيضاً
We develop some basic concepts in the theory of higher categories internal to an arbitrary $infty$-topos. We define internal left and right fibrations and prove a version of the Grothendieck construction and of Yonedas lemma for internal categories.
We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalizing the one introduced by Squier fo
r word rewriting systems. We characterize this property by using the notion of critical branching. In particular, we define sufficient conditions for an n-category to have finite derivation type. Through examples, we present several techniques based on derivations of 2-categories to study convergent presentations by 3-polygraphs.
Let $k$ be a field. We show that locally presentable, $k$-linear categories $mathcal{C}$ dualizable in the sense that the identity functor can be recovered as $coprod_i x_iotimes f_i$ for objects $x_iin mathcal{C}$ and left adjoints $f_i$ from $mathc
al{C}$ to $mathrm{Vect}_k$ are products of copies of $mathrm{Vect}_k$. This partially confirms a conjecture by Brandenburg, the author and T. Johnson-Freyd. Motivated by this, we also characterize the Grothendieck categories containing an object $x$ with the property that every object is a copower of $x$: they are precisely the categories of non-singular injective right modules over simple, regular, right self-injective rings of type I or III.
We prove general adjoint functor theorems for weakly (co)complete $n$-categories. This class of $n$-categories includes the homotopy $n$-categories of (co)complete $infty$-categories -- in particular, these $n$-categories do not admit all small (co)l
imits in general. We also introduce Brown representability for (homotopy) $n$-categories and prove a Brown representability theorem for localizations of compactly generated $n$-categories. This class of $n$-categories includes the homotopy $n$-categories of presentable $infty$-categories if $n geq 2$ and the homotopy $n$-categories of stable presentable $infty$-categories for any $n geq 1$.
Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its domain, to be
thought of as the partial identity that is defined to just the same degree as the original map. In this paper, we show that restriction categories can be identified with emph{enriched categories} in the sense of Kelly for a suitable enrichment base. By varying that base appropriately, we are also able to capture the notions of join and range restriction category in terms of enriched category theory.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
