Tenzorový součin polosvazů z pohledu teorie kategorií
| Thesis title in Czech: | Tenzorový součin polosvazů z pohledu teorie kategorií |
|---|---|
| Thesis title in English: | Tensor product of semilattices from the categorical viewpoint |
| Key words: | Tenzorový součin, polosvaz, svaz, kongruence, homomorfismus, adjunkce |
| English key words: | Tensor product, semilattice, lattice, congruence, homomorphism, adjunction |
| Academic year of topic announcement: | 2018/2019 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Pavel Růžička, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 30.09.2019 |
| Date of assignment: | 30.09.2019 |
| Confirmed by Study dept. on: | 04.10.2019 |
| Guidelines |
| Tenzorový součin spojových polosvazů s nulou je opět polosvaz s nulou. V literatuře je posáno několik způsobů jak jej definovat. Cílem studenta bude tyto způsoby analyzovat, porovnat a prostudovat tenzorový součin spojových polosvazů z pohledu teorie kategorií. |
| References |
| Anderson, J. and Kimura, N., The tensor product of semilattices, Semigroup Forum 16 (1968), 83–88.
Farley, J.D., Priestley powers of lattices and their congruences: A problem of E. T. Schmidt, Acta Sci. Math. (Szeged) 62 (1996), 3–45. Fraser, G. A., The semilattice tensor product of distributive semilattices, Trans. Amer. Math. Soc. 217 (1976), 183–194. Grätzer, G. and Wehrung, F., Proper congruence-preserving extensions of lattices, Acta Math. Hungar. 85 (1999), 175–185. Grätzer, G. and Wehrung, F., Tensor products of lattices with zero, revisited, J. Pure Appl. Algebra 147 (2000), 273–301. Grätzer, G. and Wehrung, F., Tensor products and transferability of semilattices, Canad. J. Math. 51 (1999), 792– 815. Grätzer, G. and Wehrung, F., A new lattice construction: the box product, J. Algebra 221 (1999), 315–344. Grätzer, G. and Wehrung, F., Flat semilattices, Colloq. Math. 79 (1999), 185–191. Grätzer, G. and Wehrung, F., The M3[D] construction and n-modularity, Algebra Univers. 41 (1999), 87–114. Grätzer, G. and Wehrung, F., A survey of tensor product and related constructions in two lectures, Algebra Univers. 45 (2001), 117–134. Mac Lane, S., Categories for the Working Mathematician, Springer-Verlag, NY, 1978. Wehrung F., Tensor product of structures with interpolation, Pacific J. Math. 176(1) (1996), 267-285. |
| Preliminary scope of work |
| Tenzorový součin spojových polosvazů s nulou je opět polosvaz s nulou. Obecně ale není tenzorový součin dvou svazů svazem. Tenzorový součin spojových polosvazů s nulou lze sestrojit různými způsoby. Zároveň lze z tohoto součinu odvodit několik vzájemně odlišných svazových konstrukcí.
Tenzorový součin spojových polosvazů s nulou byl intenzivně studován Grätzerem a Wehrungem se svazově teoretického pohledu. Naším cílem bude pohled na tuto problematiku z pohledu teorie kategorií. |
| Preliminary scope of work in English |
| The tensor product of join-semilattices with zero is a join-semilattice with zero. Even if both the semilattices are lattices, the tensor product is not a lattice in
general and it seems to be unclear how to treat the tensor product of lattices. Even the tensor product of join-semilattices with zero can be constructed in different ways and it leads to various related constructions. The tensor product and the related constructions were extensively studied by Grätzer and Wehrung from purely lattice theoretic point of view. Our aim will be to study the notions from categorical point of view. |