Higher Cohomologies of Commutative Monoids
نویسنده
چکیده
Extending Eilenberg-Mac Lane’s methods, higher level cohomologies for commutative monoids are introduced and studied. Relationships with pre-existing theories (Leech, Grillet, etc.) are stated. The paper includes a cohomological classification for symmetric monoidal groupoids and explicit computations for cyclic monoids.
منابع مشابه
Model Structures on Commutative Monoids in General Model Categories
We provide conditions on a monoidal model categoryM so that the category of commutative monoids in M inherits a model structure from M in which a map is a weak equivalence or fibration if and only if it is so inM. We then investigate properties of cofibrations of commutative monoids, rectification between E∞-algebras and commutative monoids, the relationship between commutative monoids and mono...
متن کاملPartially Commutative Inverse Monoids
Free partially commutative inverse monoids are investigated. Analogously to free partially commutative monoids (trace monoids), free partially commutative inverse monoids are the quotients of free inverse monoids modulo a partially defined commutation relation on the generators. A quasi linear time algorithm for the word problem is presented, more precisely, we give an O(n log(n)) algorithm for...
متن کاملSolutions to Some Open Problems on Totally Ordered Monoids
In this paper solutions to three open problems on ordered commutative monoids posed in [4] are presented. By an ordered monoid we always mean a totally ordered monoid. All the problems are related to the class of ordered commutative monoids which are homomorphic images of ordered free commutative monoids.
متن کاملEfficient Solution to Some Problems in Free Partially Commutative Monoids
In theoretical computer science, and, in particular, in automata and formal language theory, questions arise concerning words and sets of words in free monoids. Results and techniques from the study of the combinatorial algebra of the free monoid have provided an “algebraic” basis for dealing with many of these questions. In recent years there has been increasing interest in properties of words...
متن کاملMatrix representations of trace monoids
We consider trace monoids i.e., free monoids where some pairs of letters are allowed to commute. We show that such monoids can be faithfully represented by 22-matrices with integer entries if and only if it they are direct products of a free commutative monoid with a free product of free commutative monoids.
متن کامل