Details
| Original language | English |
|---|---|
| Pages (from-to) | 36-65 |
| Number of pages | 30 |
| Journal | Algebra universalis |
| Volume | 31 |
| Issue number | 1 |
| Publication status | Published - Mar 1994 |
Abstract
Although the category CLC of complete lattices and complete homomorphisms does not possess arbitrary coproducts, we show that the tensor product introduced by Wille has the universal property of coproducts for so-called distributing families of morphisms (and only for these). As every family of morphisms into a completely distributive lattice is distributing, this includes the known fact that in the category of completely distributive lattices, arbitrary coproducts exist and coincide with the tensor products. Since the definition of tensor products is based on the notion of contexts and their concept lattices, many results on tensor products extend from complete lattices to contexts. Thus we introduce two kinds of tensor products for arbitrary families of contexts, a "partial" and a "complete" one, and establish universal properties of these tensor products.
Keywords
- AMS Mathematics Subject Classification 1991: 06A23, 06D10, 18A30, complete homomorphism, complete lattice, completely distributive, concept lattice, conceptual morphism, Context, tensor product
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Algebra universalis, Vol. 31, No. 1, 03.1994, p. 36-65.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Tensor products of contexts and complete lattices
AU - Erné, Marcel
PY - 1994/3
Y1 - 1994/3
N2 - Although the category CLC of complete lattices and complete homomorphisms does not possess arbitrary coproducts, we show that the tensor product introduced by Wille has the universal property of coproducts for so-called distributing families of morphisms (and only for these). As every family of morphisms into a completely distributive lattice is distributing, this includes the known fact that in the category of completely distributive lattices, arbitrary coproducts exist and coincide with the tensor products. Since the definition of tensor products is based on the notion of contexts and their concept lattices, many results on tensor products extend from complete lattices to contexts. Thus we introduce two kinds of tensor products for arbitrary families of contexts, a "partial" and a "complete" one, and establish universal properties of these tensor products.
AB - Although the category CLC of complete lattices and complete homomorphisms does not possess arbitrary coproducts, we show that the tensor product introduced by Wille has the universal property of coproducts for so-called distributing families of morphisms (and only for these). As every family of morphisms into a completely distributive lattice is distributing, this includes the known fact that in the category of completely distributive lattices, arbitrary coproducts exist and coincide with the tensor products. Since the definition of tensor products is based on the notion of contexts and their concept lattices, many results on tensor products extend from complete lattices to contexts. Thus we introduce two kinds of tensor products for arbitrary families of contexts, a "partial" and a "complete" one, and establish universal properties of these tensor products.
KW - AMS Mathematics Subject Classification 1991: 06A23, 06D10, 18A30
KW - complete homomorphism
KW - complete lattice
KW - completely distributive
KW - concept lattice
KW - conceptual morphism
KW - Context
KW - tensor product
UR - http://www.scopus.com/inward/record.url?scp=0042213634&partnerID=8YFLogxK
U2 - 10.1007/BF01188179
DO - 10.1007/BF01188179
M3 - Article
AN - SCOPUS:0042213634
VL - 31
SP - 36
EP - 65
JO - Algebra universalis
JF - Algebra universalis
SN - 0002-5240
IS - 1
ER -