About 894 results
|This chapter introduces the main object of study, the notion of M-precategory. The |
terminology “precategory” has been used in several different ways, notably by
Janelidze . The idea of the word is to invoke a structure coming prior to the ...
Andrew D. Gordon - 2003 - 440 pages
|The solution adopted by Leifer  and later by Milner  is to introduce a |
notion of a well-supported precategory, where the algebraic structures at hand
are decorated by finite “support sets.” The result is no longer a category – since ...
George Janelidze, Bodo Pareigis, Walter Tholen - 2004 - 570 pages
|First we define the notion of precategory, which is just an internal reflexive graph |
with composition. Next we define precategory with associativity (up to
isomorphism) and call it associative precategory. Afterwards we define
V. N. Gerasimov, N. G. Nesterenko, A. I. Valitskas - 1993 - 195 pages
|A (pre)category over O is called representable if there exists a univalent functor |
from this (pre)category into a commutative algebra with identity considered as a <
I>-category with a single object. A (pre)category 3 over O with a partial order on ...
|To achieve this, we use the notion of a precategory, which is a technical synonym |
for a system of generators and relations. It already appeared in Joyal and Street
study of monoidal categories  under the name of tensor scheme or valuation ...
Vladimir Alekseevich Smirnov - 2001 - 235 pages
|A chain precategory X consists of a family of objects (X) and a family of chain |
complexes Hom(X1,X2) (whose elements are called morphisms from X1 to X2)
given for each pair of objects X1, X2 E X. Definition. A prefunctor f:X — » y from a
Associate Professor John C Baez, J Peter May - 2010 - 292 pages
|We begin with the definition of a Segal precategory. Definition 5.1. A Segal |
precategory is a simplicial space X such that Xq is a discrete simplicial set. As
with the Segal spaces in the previous section, we can use the Segal maps to
Sylvie Paycha, Bernardo Uribe - - 255 pages
|If V is a dg-vect H(V) denotes the homology of V. A dg-precategory C consist of a |
collection of objects Ob(C) and for any x, y C Ob(C), a dg-vect C(x, y) called the
space of morphisms from x to y. A dg-category C is a dg-precategory together
|Definition 5.7.12 A full sub (pre) category D of a (pre)category C is called a conic |
sub(pre)category (notation: T> C(0) C) if Vw C ObV\/v(C*(u,v) ^0=>v£ ObV). Here
is a typical example. Definition 5.7.13 For a (pre)category C and u £ ObC the ...