Generalized Enrichments of Categories for Operads
| Autor: | Zizhu Ma |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Algebra and Number Theory
Functor Applied Mathematics Monoidal category Symmetric monoidal category Mathematics::Algebraic Topology Algebra Morphism Category of small categories Mathematics::K-Theory and Homology Mathematics::Category Theory Discrete category Enriched category Mathematics 2-category |
| Zdroj: | Algebra Colloquium. 14:61-78 |
| ISSN: | 0219-1733 1005-3867 |
| DOI: | 10.1142/s1005386707000077 |
| Popis: | Most enriched categories also have an ordinary category structure which is compatible with the enrichment on them. In this paper, enrichments in a monoidal category are generalized to arbitrary categories. These specialize to the classical enrichments when sets are regraded as discrete categories. We also generalize the definitions of PROs and PROPs as some generalized enrichments of categories. Then an operad in some monoidal category corresponds to a generalized PROP. Algebras of operads induce some special kind of monoidal functors. In the category of small categories, we construct several operads to define lax monoids and lax commutative monoids which are formal descriptions of natural associativity and commutativity. Using this identification, operads and their algebras can be studied by lax commutative monoids and morphisms between them. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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